Some time ago I wrote down "lie one on" with this meaning for a flashcard; I must have read it somewhere, probably in a book, but I don't remember where. After a couple of months I wanted to look up the phrase again, but couldn't find it anymore. It doesn't seem to be listed in a single dictionary (also not in my American slang dictionary) and I can't find it on the Web. Does this expression really exist? Unfortunately, because I don't remember where I found it I can't give any context.
The expression is "tie (not lie) one on."
Its origins are somewhat disputed, with some claiming that it references a cowboy tying his horse to a hitching post before going into a saloon to get drunk.
Regardless, yes, it is a euphemism for getting drunk or having an alcoholic drink.