The Rat was an unnamed anthropomorphic rat character from The Lenny Lego Movie who, in the first installment, anxiously offers to join Lenny in defeating Clonebot. Lenny agrees, and the character rushes off to pack his bags to join him on his journey. He was never seen or mentioned in the film again. In the post credits scene for the sequel, he finally reaches the gang's original destination (unaware that their plan is actually long complete by now), and waits for them to arrive. In the post-credits scene of the third film, he calls Lenny (it is left unexplained how he managed to get Lenny's phone number) and demands to know what's taking him so long, still waiting for him to arrive, and still unaware that their plan there is now even longer (about two years) complete at this point. He then falls off a ledge as the call abruptly ends; his fate from the fall is left unexplained. Failing to remember meeting the character before, Lenny casually assumes it's a wrong number.
There are two known plot-holes in the Lenny Lego series regarding this character. Upon confronting Lenny in the first film, Mammoth Duncan (the prototype identity of Mammoth Duncan's character), who is naturally terrified of rats, was was present during this confrontation and never freaked out upon greeting the character. It was even portrayed in the show around that time that Mammoth was indeed terrified of rats.
A less contradictionary plot-hole regards his cameo at the end of the third is his waiting location in Clonebot's base, which Lenny, as well as a few other characters, were actually located earlier in the film. However, it could be assumed that the character was busy (perhaps sleeping) somewhere and failed to recognize his presence. Also, it should be noted that a majority of Lenny's time spent there was captured in the basement, and actually spent much less time elsewhere, such as where this character was waiting the whole time.
"The Rat" was a film-exclusive character; he never appeared in any episodes or even either of the spin-off films.