How can I treat my red and inflamed inner eyelids before LASIK?

It seems like you are having some symptoms suggestive of inflammation around the surface of the eye. This could be due to dry eye, blepharitis or allergic conjunctivitis, to name a few possibilities. It would be best to seek the opinion of an ophthalmologist who would be able to conduct a thorough exam of your eyes and direct the right treatment for your symptoms.

With regards to blepharitis, it is true that warm compresses can be helpful. However, often times chronic cases may require medication in the form of topical antibiotic and steroids. Best to seek the opinion of an ophthalmologist to know what treatment is required in your case.

there are several possibilities for the problem you mention ie redness and slight swelling just on the inner part of the under surface of the eyelids.

It may be nothing pathological (sometimes certain parts of the eyes/eyelids may look a bit redder but be normal), or it may be issues like dryness or eyelid inflammation/blepharitis.

Without knowing what the problem is for sure, it is difficult to know what else to do to make it better.

If you are intending to go for LASIK eventually, I would suggest you pay a visit to a doctor who also performs LASIK and seek his/her advice, including about your eligibility and whether any pre-treatment of your eyes/eyelids is necessary.