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I understand you are concerned about the drug to drug interactions and also L-lysine role in helping dizziness. L-lysine has no established role in helping with dizziness. Although there are some studies showing benefits to some extent, in patients with chronic anxiety, especially when taken with L-Arginine. Because there is no reported interaction between the two drugs, you are concerned about alpha-lipoic acid and L-lysine. We cannot say for sure if an interaction exists or not.
It may be because no much research is conducted on these two chemicals. Lysine, however, can increase the amount of calcium absorbed in the body, so avoid taking large amounts of calcium supplementations along with lysine. Anti-diabetes drugs have strong interaction with alpha-lipoic acid, and anti-cancer drugs (chemotherapy) has mild to moderate interactions reported. I hope it helps. Ask more if you need further assistance. I would be happy to help.