It's not the only one that matters and there's no belt.
So, the lineal champion is the man who beat the man who beat the man. Usually the lineage is started when a fighter becomes the undisputed champion in their weight class. The fighter who beats that fighter is the new lineal champion and so forth.
But it's not the only one that matters because eventually at some point the lineal champion isn't going to be the consensus champion. Let me give you an example.
When Iron Mike Tyson was destroying everyone in his path and picking up championship belts along the way, there was a guy called Michael Spinks walking around with lineal status after he defeated the former lineal champ Larry Holmes. Although Mike was the undisputed heavyweight champion and was a heavy favourite when he got in there with lineal champ Spinks, it was only after Tyson knocked Spinks out that any remaining arguments had been settled about who was the number one heavyweight in the division.
When Wladimir Klitschko "became" lineal champion it wasn't because he beat the man OR because he became undisputed, his is one of the stranger crownings but he was crowned lineal champ because of his dominance and long reign over the division, it was agreed that he was the man and since the previous lineal champ had retired, the only way Wladimir could have become undisputed at the time would have been to defeat his brother in the ring and this was an unreasonable demand to make so Wladimir was just given the lineage.