You can use lactic acid as an optional exfoliation step while checking rinse-off versus leave-on directions and keeping your routine simple without chasing a stronger formula.
First read the product's intended use because lactic acid may be an exfoliating ingredient or a pH adjuster and an ingredient listing alone does not define a routine.
If it is an exfoliating product, check whether it is rinse-off or leave-on. Follow that product's contact time rather than borrowing instructions from another acid.
You do not need an extra exfoliation step just because a familiar moisturizer lists lactic acid among its ingredients.
There is no single schedule that fits every lactic acid product. Follow the label and assess comfort before increasing use within those directions.
Do not leave a rinse-off acid on overnight or add extra applications to chase faster results.
If burning or persistent stinging develops, stop. More discomfort is not evidence of better exfoliation.
Keep a familiar cleanser and moisturizer so you can judge how one new product affects your skin.
Follow FDA AHA precautions: use sunscreen and protective clothing and limit sun exposure during use and for a week afterward.
A simple routine that stays comfortable is more practical than adding several exfoliants at once.
Avoid adding scrubs, other acids and retinoids at the same time initially for practical irritation management.
This is a practical approach to irritation management rather than a claim that every combination is chemically incompatible.
Ask your treating clinician before adding an acid around prescription treatment or a skin procedure.