This is an interesting question.
The short answer about lactones vs. lactic acid is: Yes lactones are structurally related to lactic acid, but, no, the kavalactones in kava that you drink won't be converted to lactic acid by your body's metabolism.
That doesn't mean kava isn't causing your symptoms. Kava is a drug with a wide array of effects on the nervous system and body. So it certainly is possible that it could be interacting with your condition in some way that might aggravate your symptoms.
The long answer to the relationship between kavalactones and lactic acid is:
Lactic acid is a simple organic acid that is produced by bacteria from sugar, and also produced in your body from sugar. More of it is produced during exercise when the oxygen supply to cells is limited, and if too much of it builds up it can be toxic, but it is a normal part of human metabolism. Lactic acid was first discovered in sour milk, which is where its name comes from.
Lactic acid belongs to a category of molecules called alpha hydroxy acids that are commonplace in living organisms and in foods, etc. Other examples of alpha hydroxy acids include citric acid in citrus, and malic acid that is found in fruits such as apples and grapes used in winemaking. Malic acid is sort of like two lactic acid molecules stuck together. In winemaking they use a process involving bacteria that breaks malic acid down into lactic acid. (See
https://en.wikipedia.org/wiki/Malolactic_fermentation )
Lactones are a related category of molecules that have a ring shape. They can be synthesized from alpha hydroxy acids (which are not ring shaped). Lactones were discovered and named in 1844 by a French dude who was the first to synthesize a simple lactone from lactic acid. Ref.
https://en.wikipedia.org/wiki/Lactone#Etymology
Kavalactones are lactones, but they have a complex structure that distinguishes them from other lactones. And like other lactones, it is possible to synthesize kavalactones from alpha hydroxy acids. For example dihydrokavain can be synthesized from malic acid. (Ref.
https://www.tandfonline.com/doi/abs/10.1080/00397911.2018.1489057 )
So, the relationship between lactic acid and kavalactones is: lactic acid belongs to a category of organic acids, other members of which can be used as precursors to synthesize kavalactones. However in nature, kavalactones are synthesized by a complex enzymatic process. (Like, really complicated. See
https://par.nsf.gov/servlets/purl/10166488 ), not like the relatively simple syntheses that humans have learned to do.
Then you also might wonder whether when your body metabolizes kavalactones, mightn't they be broken down into smaller molecules including lactic acid, since they can be synthesized from things similar to it? But as far as I understand it, the answer is no. It
is possible synthetically to break down lactones by a reaction involving sodium hydroxide. So you might be able to break kavalactones down to malic or lactic acid by some laboratory process. But that is not how your body metabolizes them. Because KL's are not naturally occurring in humans, our bodies see them as exogenous, which means they are metabolized using the system for eliminating toxins and foreign substances,
not via the metabolic system in cells that produces lactic acid from sugar. This is the mechanism that metabolizes most drugs in the liver. And the way that mechanism works generally is not by breaking drug molecules down into smaller parts, such as lactic acid, but instead by conjugation, which means sticking a large molecule such as glutathione onto them to render them inert and water soluble so that they can be eliminated, peed out. For anyone wanting more technical specifics, here is a recent paper where they determined the metabolites of kavain:
Enzymes and Pathways of Kavain Bioactivation and Biotransformation. Chem. Res. Toxicol. 2019, 32, 7, 1335–1342 . All of them appear to be large conjugated molecules as expected.
So, having made a long story long, yes, lactic acid and kavalactones are structurally similar, but as far as I know that similarity is not really relevant to what is going on when we metabolize the kavalactones that we drink.