Libel is a noun meaning the publication of a false statement that damages someone’s reputation (see libel or slander).
Liable is an adjective which means responsible by law for something – “He is liable for the damages in the case” or likely to do something – “The cat is liable to tread on the keys and insert characters into your document, so it’s best to keep him off the desk”. You can also use liable to in the sense of “likely to experience something” (usually something undesirable) – “This area of low-lying land is liable to flooding”. (Note: I don’t like this last use – I’d be tempted to change it to “liable to flood” but that’s just my personal opinion).
You can combine them, of course – “The newspaper was found liable for all charges in the libel case brought by Mr. Brown regarding his damaged reputation and the lies that the paper had printed”.