I haven't done LRS but I don't see a reason why you couldn't make that measurement over only a few days, if you keep this method consistent through out all your populations. Just as a control you might have to do a complete LRS to see if you get any patterns in their egg laying behaviour, which I assume/believe is a decreasing pattern over time but just check the pattern of your WT and make sure your food is the same throughout all your experiments as changes in yeast % can completely distort your results as fly lay eggs like crazy when given yeast!! so use the same batch of fly food.
Although I'm no expert at this, if you look at female ovaries and do some molecular/phenotypic characterisations, you might get some interesting data if you are already observing a huge difference between your populations although you would have to look at the literature for this but having played around with these stuff a little, you find a surprising amount of data! This is in a way nice since you take the males out of the equation as the reproductive fitness could be compromised by either males or females in a population. To determine this you need to cross the males and females of your population of interest to WT flies and count the embryos (although this is slightly dangerous since if males are not performing well, females can lay lots of unfertilised eggs, blanks, and they are indistinguishable from fertilised egg so maybe count the hatched offspring and immediately discard them although that presents its own set of challenges and variables and to be honest its not likely to happen since you usually get this blanks in virgin females that have not yet courtshiped). If you observe lets say no changes in embryo numbers when your male populations are crossed to WT females but significant changes when females are crossed to the WT males, you would know the problem is with the males in your population.
Hope this helps!
EDIT: So I looked a bit further into this and came across this paper (http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0024560). If you look at Fig 6, I think it answers your question. I'm basically quoting the paper here. They measured the correlations between adult LRS and cumulative and short-time measures of fecundity and offspring production. Correlations of the short-time measures of fecundity and offspring production with adult LRS were highly dependent on the time of measurement. For young females the correlations were low, but when measured from older females, the correlations were much higher (up to 0.67 for short-time fecundity and 0.83 for short-time offspring production). For both short-time fecundity and short-time offspring production the highest correlations with adult LRS were reached when the female age was about 50 to 80 days. The length of the time frame had only a minor effect: the correlation of the 10-day measure with adult LRS was generally only slightly higher than that of the 2-day measure. The short-time measures performed well in comparison to the cumulative measures of fecundity and offspring production. So in short if you let your females age a bit and measure their fecundity, then it should be representative of their LRS.