There has been some discussion of what happens to the LCL pumped into pilots on the EvaGeeks forum; I found threads from 2009 and 2014. (Needless to say, these contain spoilers for the series.)
It appears that there has never been an actual explanation for this. However, after reading another thread on LCL, I can make some guesses.
I think maybe LCL is absorbed into the body going by what happens during Third Impact. to quote the wiki (spoiler because it is end of the original anime series stuff)
Source: LCL (6th paragraph)
in real life the human body can absorb water after it enters the body and in the first X-Men we see
so in a sense one could think of LCL like Water in that