I chose this name as an abbreviation of amateur lexicographer or amateur lexicologist. It could also be construed as "amat lexeis", or "he loves words". (Lexis is a Greek word meaning "word", and was occasionally found in post-Classical Latin. The Greek inflection would most likely be followed in Latin, and I believe that the accusative plural would therefore be "lexeis" - but am not certain, so corrections are welcome.)
On rereading the above, I see that it's nonsense because if my name were based on Latin and Greek, it would need to be Amatlexeis instead of Amatlexico - unless we also borrow the Greek word "lexicon" into Latin.
I live in Oxford, England, and am a member of Sidney Sussex College, Cambridge.