It would be Lazarus' first encounter with actively studying ASL. L is a character who is shown to be highly (and unrealistically, but this is a fictional anime genius) multilingual in canon and capable of taking in a lot of information very quickly. Having solved 1,000 of the world's most difficult cases, even if only one of those required comprehension of ASL (or any other language), he would have put effort into learning it, and probably seen ASL in particular as very useful for other reasons (since he relies on a handler and they share most of their intel) a method of communicating silently would have its merits for a detective under more than a few circumstances.

It is a headcanon/reasonable assumption echo (like most of his other language echoes); unfortunately we get to see a very small portion of L's career in canon, so there's 17 years completely unaccounted for where all we know for sure is that he was being an awesome detective and solving 1,000 distinct cases while acquiring a lot of random and surprising skills (like Capoeira and flying a helicopter, which are hard canon). Of all these random skills, languages are probably the most useful and reliably reasonable to headcanon.

If this isn't OK or simply too farfetched, I'd like to alternatively have him echo back his ridiculously quick learning curve via Wolpertinger encounter (Tier 2 would be OK, since it's a big one) so he can go about picking it up.