He got em. It was played to perfection and be used every tool in the shed. Literally the best anime drama series ever. The symbolism in the series is epic. Down to the washing of the feet. It's biblical as L knew his time was up and betrayal was imminent
L tried to prove that the 13 day rule is fake by having a criminal write a name and still be alive for longer than that. This would pretty much end the case and Misa and Light are done. Obviously Rem couldnt allow this and had to step in, and L knew that something would happen if he tried this but its not like he had any options left. It was a last attempt but he knew he was probably going to die. I dont think L would even think about killing Light before confirming this for sure, that would be cheating. He might aswell have killed him in episode 10 then. Killing Light without beating him in the game is basically the same as losing the game. Also, the scene is a reference to Jesus washing Judas' feet knowing he would betray him. Theres lots of religious imagery in the show as you might have noticed, the Apple representing the Death Note/forbidden fruit and Light taking a bite in the first op is pretty on the nose for example. Or Naomi Misoras pose in the op referencing Michelangelos Pietà.
Notice how in episode 10, the tennis match was a personification of this whole battle between Light and L, where they seem to be friendly to each other but I are actually plotting each other’s downfall… and light won
L has become like top 5 characters in anime I ever seen, at least he died knowing he was right about light being kira, he just needed evidence to prove it. (He is dead btw) also his name is L Lawliet