I cross shopped the LC and AMG and walked away with Lexus in the end. There where pros and cons to each vehicle but the pros for the Lex outweighed those of the Merc. In the past I had a Merc S550 and when running properly it was a dream to drive but had some gremlins that made for a few too many trips to the dealer. Not to say all Mercedes has problems but it is well documented who is consistently the king of reliability (Lexus) and who is mid pack (Mercedes). Men lie woman lie but numbers don't as the saying goes. Both cars look like spaceships on the road and will garner attention if thats your bag. The AMG pulls harder and faster but the Lex doesn't really leave you wanting and the soundtrack is sublime when running up the tach on each.
The AMG was a super tight fit for me at 6ft 2in 230lbs but the Lex is a perfect fit. Every ride is worry free and the Lex makes me feel special when I drive it, it was the sensible choice for me. Go drive them both and see which one feels right to you. Good luck!