This is primarily a linguistic question and I am answering it on the basis that it will be migrated to Stack Exchange, English Language and Usage.
The question is whether, in the context of a report describing (otherwise unspecified) student work, the phrase “aseptic technique” can be used without an article, or whether it requires the definite or indefinite article. This is a question of meaning and usage, and, without using any technical grammatical terms, can be answered by anlysis of scientific publications and by analogy.
“The aseptic technique” (definite article)?
The definite article would normally be used in this type of situation if reference was to one specific clearly defined technique. As an anlogy I would take ‘The Heimlich manoeuvre’ (where ‘manoeuvre’ occupies an analagous position to ‘technique’. Clearly the phrase does not refer to a standard defined procedure like the Heimlich manoeuvre, but merely that the work was performed asceptically (i.e. under sterile conditions). So in this context the definite article is certainly not necesary. In some circumstances employing sterile conditions requires satisfying certain enumerated criteria (example below), in which case the definite article may be used.
“An aseptic technique” (indefinite article)?
I think that this is possible but not obligatory. The use of the indefinite article indicates that the asceptic technique used was one of several possible. Although sometimes this would be used in the context of a limited number of items, this is not a necessary requirement. Analogies with a different adjective would be “she executed the dive with a graceful technique”. Here, the article is (almost) obligatory, but less so in the case of “she showed superb technique in executing the dive”.
“Aseptic technique” (no article)?
As the last example shows (“she showed superb technique in executing the dive”), omitting the article is perfectly acceptable in analagous phrases. I would say it is perfectly acceptable in this case.
The arguments above are only useful to the extent that they reflect actual practice. A quick internet search brought up an interesting example in which both no article and the indefinite article were used in the same text. This is the entry for Asceptic Technique on a website called Healthline.
The second paragraph omits the article:
Aseptic technique is a method designed to prevent contamination from microorganisms.
But when it gets down to specifics:
According to The Joint Commission, there are four chief aspects of the aseptic technique
So unless your friend was referring to ‘The Joint Commission’ (which I doubt) there is nothing wrong with that sentence of her lab report.
Other Professional Examples
ThermoFisher Scientific — no article
Aseptic technique, designed to provide a barrier between the microrganisms in the environment and the sterile cell culture, depends upon a set of procedures to reduce the probability of contamination from these sources
Nuffield Foundation — indefinite article (implied by use of ‘any’)
There are some general rules to follow for any aseptic technique.
ANTT — definite article used in reference to a specific named technique
Aseptic technique is the most commonly performed infection prevention procedure in healthcare; it is also probably the most critical. This article looks at the Aseptic Non Touch Technique (ANTT) model for reducing healthcare-associated infections
(You could argue that the definite article refers to the model, rather than the technique, although I think if you omitted ‘model’ you would be left with an example like the Haemlich manoeuvre. In any case the English in this article is appalling — “infection prevention procedure” gives a foretaste of the stylistic horrors that follow.)