I've owned quite a few lacoste t-shirts, not knowing if they were genuine until I purchased one from Neiman Marcus. I immedietly saw what a "real" lacoste shirt means:

Its very simple, Look at the alligator: A real lacoste alligator actually started out as a seperate piece that is then sewn onto the shirt/cap/jacket etc. If you would turn the fabric inside out you will not see the alligator at all- you will only see where it is attached to the fabric with a few stitches. You can probably remove it entirely. The fake  Lacoste shirts  have the gator embroidered  onto the fabric itself. If you turn the shirt inside out you will see the entire alligator sewn into the fabric. You cannot remove it- it is part of the shirt. 

I'm pretty sure that all genuine Lacoste products are made this way, as I've noticed that on all my caps and shirts that I bought in Lacoste stores have the alligator as such, whereas the ones I've bought from ebay and other no-name stores have the alligator as an embroidery.

Unfortunately, It is hard to see this small detail over ebay. I doubt any seller is showing you a picture of the inside of their t shirts.;) But next time you are in an upscale shopping mall (bloomingdale's, nordstrom's etc) check out this detail on their shirts and you'll learn very quickly what a real Lacoste shirt is.