From the "Technical guide for the elaboration of monographs" by EDQM, edition 7, 2015, page 25:
Where the counter-ion of an active substance is formed from a lower organic acid, a test for related substances of the organic moiety is usually not considered necessary (for example, magnesium lactate used as a source of magnesium).
What is the meaning of "lower organic acid"? An organic acid of simple composition, with a short alkyl group?
The term doesn't seem to have an official IUPAC definition however several sources agree that the lower organic acids are those that are soluble in water.
In the simplest case this could just refer to the first 5 carboxylic acids (C1-C5): methanoic (formic) acid, ethanoic (acetic) acid, propanoic acid, butanoic acid and pentanoic acid.
What is less clear is whether small water soluble acids such as lactic acid and tartaric acid are counted. (The context of the quote in your question suggests it may well be, though it's wording isn't overly clear)
Since the phrase has no official definition I think it's probably safe to use it as you see fit, ensuring you define what you plan on calling a lower acid and use it consistently. You will equally see people refer to lower amines or halides, which in the same way isn't a well defined phrase but just lets people vaguely define a group of compounds.
