The expression "like it or lump it" means that something must be accepted because the situation isn’t going to change. Oftentimes, idioms are used as a kind of linguistic shortcut. As long as all the speakers involved understand an idiom’s meaning, it can be a very efficient way of communicating. Some idioms are easy to understand even for those who may not have encountered them before, but others are about as clear as mud. "Like it or lump it" falls into the latter category; unless the listener already knows its meaning, there’s a good chance that the idiom won’t be a shortcut at all.
This saying is typically used casually. Friends or people who work at the same professional level might say it to one another, but an employee or student would never use the expression with a boss or teacher. It can sound a bit harsh or rough to a non-native English speaker. It’s often preceded by a short, dismissive phrase. For example, someone who is complaining about income taxes might be brusquely told, “Yeah, well ... like it or lump it.”
Looking for logic in the expression isn’t likely to be a very satisfying task. This is largely because of the presence of the word lump. In common parlance, a lump is a bump of some sort, generally misshapen and unappetizing. Naughty children are given a lump of coal, and two guys in a fight try to give each other lumps. With this in mind, there seems no logical connection between liking something and lumping it, unless the expression can be interpreted to mean that either a person can like something or fight it.
This expression is very old, and like most idioms whose origins are shrouded in the mists of time, some of its individual words have shifted in meaning. In the 16th century, lump or lumpe meant to complain or grumble. By the early 19th century, that meaning had fine-tuned somewhat into being unhappy with or disliking something. Now, the meaning of the idiom "like it or lump it" becomes transparent.
It is interesting to speculate why some newly coined idioms enter the linguistic stream, become so popular they are found in all manner of pop culture from films to news reports, then just as quickly vanish, while other idioms with obscure origins stick around forever. No one comments that something is "out of sight" anymore, though once upon a time, it was on everyone’s lips. Perhaps the persistence of the expression "like it or lump it" can be attributed simply to the balanced, nearly identical sounds in the words.