Given that each trophic level of the food chain has a decrease of 90% of available energy, would it be fair to say that 1kg of lettuce has more energy than 1kg of beef? If it's not true, can you explain the reason?
1kg of beef has more energy than 1kg of lettuce but it isn't directly related to the trophic level energy loss.
Given that each level of the food chain has a decrease of 10% of available energy
You're all mixed up here. What the rule is saying is that if you start out with n units of solar energy, you lose 90% of it for every trophic level it passes through; Only 10% passes through as stuff that "stays around" materially (i.e. used to build the structure of the organism rather than being burned away as fuel to keep it alive). That means that it takes about 10x more energy to produce the same amount of edible calories in beef than it does in vegetables and grains, if they are separated by one trophic level.
It's not talking strictly talking about the energy density in food, but instead about how wasteful it is to produce the food containing those edible calories from the point of view of the total solar energy invested. For the same solar energy, you can feed a lot more people calorie-wise with vegetables and grains than beef.
It's kind of like thinking how many vegetables a rabbit eats over the couple years of its life from birth to when the rabbit becomes food for you. How long could you feed yourself on those same vegetables? Weeks maybe? How long could you feed yourself, if you ate the rabbit? A few days at most. You can imagine all those vegetables weigh more than the rabbit, but supply more energy than the rabbit meat, while the same mass of rabbit flesh has more calories than the same mass of vegetable. The rule isn't talking about calorie density of food.
Obviously, there are complicating factors, such as the actual composition of the food, since that determines calories and nutrition (which isn't related to solar energy).
The reason the same mass of beef has more energy is that 10% that sticks around keeps on accumulating. This is also the reason toxins accumulate in animals higher up the food chain. A little plankton might have a tiny bit of mercury in it, but a small fish might eat a billions of plankton. And, then a large fish might eat a thousand small fish. And, you might eat one large fish. If that mercury stuck around in everything that ate it, all that accumulated mercury ends up in you.
The so-called '10% law' is a common, albeit very rudimentary, rule-of-thumb in foodweb analysis. It's commonly attributed to Raymond Lindeman, though he cited a wide range of ratios in natural systems. The point it's trying to make relates to the transfer of energy between trophic levels, not about the energy density of plants or animals in each trophic level.
The '10% law' would generally be parsed as 'it takes 10 kilojoules of energy stored in grass to make one kilojoule of energy stored in a herbivore, and 10 kilojoules of herbivore to make one kilojoule of a carnivore'.
Energy density of various foods is routinely measured. The US Department of Agriculture estimates the energy density of beef (15% fat, broiled) at 10470 kilojoules per kilogram, and the energy density of lettuce (Romaine) at 720 kilojoules per kilogram. One kilogram of lettuce clearly provides less food energy than one kilogram of beef.
The (food) energy in 1kg of lettuce or 1kg of beef depends on each's composition, not on its trophic level. Normally we can digest fats, protein and carbohydrates, but other organisms like certain bacteria and fungi can even digest components like fiber and cellulose than we can't. Water doesn't provide any energy, but is still part of an item's weight, so food scientists normally calculate available energy for people based on the dry weight of fat, protein and carbohydrates, using average calories per g for each of the 3 classes of components.
The trophic levels/food chain 90/10 rule refers to how much biomass is produced in an ecosystem, not the energy content of a certain piece of that biomass.
Note that the decrease in food energy from one trophic level to the next is 90%, not 10%, if only 10% of the energy is actually passed on to the next level.
To compare 1 kg of lettuce with 1 kg of beef is not a very fair comparison for several reasons.
Most cows don't "beef up" on lettuce; they are usually either grain-fed or grass-fed.
Cows don't get their calories directly from the foods they eat to begin with--they eat to feed the bacteria in their stomachs, from which they derive their own sustenance. (This not being a direct transfer may have some complications in terms of whether one should consider this to be one trophic level or two.)
Because of the energy transfer ratios, the cow will eat many kilograms of food to put on one kilogram of weight. But in the process, the food is also changed in its form from being mostly simple carbohydrates to having considerably more fat and protein which are higher caloric-density foods.
Clearly, 1 kg. of beef will have more food calories than 1 kg. of lettuce.
Just to complement @DKNguyen's excellent answer, think about this: if you were raising cows on lettuce, how many cows would you have and how much lettuce would you have? Obviously you could not have more cows than lettuce, because then you couldn't feed them. That's another rule of biology: "you'll eventually always have less predators than prey" (because when the number of prey falls below the number of predators, the predators will starve to death and reduce their numbers). So there you have it: the total amount of lettuce you would have would much more than compensate for the total amount of cows you were raising. The total amount of energy in lettuce would be far superior than the total amount of energy in beef.
But clearly, in the real world, we do not raise cows on lettuce. However, the same principle applies to whatever we use as cow feed.
Side note: I hope that makes you think about how very inefficient (and wasteful) it is to consume meat on such a large scale as we do.
only about 10 percent of energy stored as biomass in a trophic level is passed from one level to the next.
"biomass in a trophic level is passed from one level to the next" is a lot of words to say that the cow eats the lettuce. This conversion from lettuce to beef is a lossy process. Similarly, if you hypothetically continue to farm down the trophic pyramid, growing bears and feeding them your cows, it's likely to take about 10 kg - likely more - beef to produce 1 kg of bear meat.
A 300 kg cow will give about 180 kg of beef. But growing that animal for approximately two years is likely to require about 1,300 kg of grain and 7,200kg of silage/roughage. The "90%" number is a rough approximation; 180 kg is 13% of 1300, the silage or pasture gazing can count for something and bring it reasonably close to the 10% rule of thumb. Intentionally bred animals like some fish or poultry can be more efficient than beef.
The important thing to consider is that when you drive by unimaginably huge fields of grain being farmed 40 feet at a pass by massive combines and wonder how people could ever grow hungry, be aware that we're wasting a lot of those calories by turning them into beef.
As a side note, the cow will (generously) average about 40 liters (40 kg, 10 gallons) of water per day for those 2 years, for a total of (730 days * 40 kg water/day) / 180 kg beef) = 160 kg water actually drunk by the cow per kg beef produced. That's a lot, but that's not counting all the water used to grow that grain and roughage (and lettuce)...generous numbers for that growth is how you end up with insane quantities like 10,000 liters of water per kg beef. If you assume that the water in the cow's urine is recycled to the water table and that the water that drains into the soil goes into the same aquifer or transpires from the grain goes back into the water cycle, the numbers are much more manageable - but it's still a lot of water. If you substitute for the veggie burger at dinner, feel free to leave the water running while you brush your teeth, you've saved more water than a week's brushing by not consuming that meat.
As a bonus side note: At a high level, both protein and carbohydrates have an energy density of 4 (kilo)calories per gram. Fat has an energy density of 9 calories per gram. However, 1kg of raw beef is not 1000 grams of metabolically available protein, it's actually a combination of water, collagen, elastin, about 200g protein, and about 50g (depending on the cut and cooking process) of fat. Similarly, 1 kg of lettuce is mostly water, quite a bit of indigestible cellulose, and about 30g of actual caloric carbohydrates. So your question could also be interpreted as "Does something containing 30g of carbohydrates have more energy than something containing 200g of protein", and the answer to that is a definitive "no", the former has 120 calories and the latter has 800 calories.