This is an old fashioned way of simply saying that somebody is lying. Most of the time, the liar is really trying to convince the person of that lie. The lie may be repeated, the liar may argue, and even tell more lies to reinforce the original lie. Beating somebody down to a lie can also be expressed as beating somebody down to a pack of lies, when several different lies are told.
He beat me down to a lie. He said he hadn't been drinking and the whole time he smelled of alcohol so strong you wouldn't believe it. It's really sick how he can be beating somebody down to a lie like he does. I think he has himself convinced he's telling the truth.