Firstly the story took place hundreds of years after Sanhedrin stopped judging capital cases.They stopped doing so even before they disbanded.
Secondly, even had Sanhedrin been around and even assuming Reish Lakish was guilty of murder (do you have a source that he was? the Gemorah does mention him killing people but they were murderers who were going to kill him )he would have needed two kosher witnesses AND a warning a few seconds before he committed the act of murder that he was doing a capital. offense. It's safe to assume he didn't meet that criterion. He would have had to meet the same criteria for lashes. Furthermore, theft is not a crime that one receives lashes for.
One can question if he paid back what he stole. There is no reason to assume he didn't but if he didn't it may inter alia be because of the Gemorah which says that if a thief is looking to do Teshuva we don't accept the return of his stolen items out of concern that he may decide against doing Teshuva due to the difficulty involved. There are also other reasons why he may not have been halachicly obligated to pay back.
As far as why Sanhedrin didn't use their (nonexistent at the time) secular authority, perhaps that question could be asked about before he did Teshuva but afterward? Sanhedrin was not in the business of using extrajudicial powers to kill people who clearly had done Teshuva.
Decades before they disbanded they stopped judging capital cases because there were too many people who halachicly deserved the death penalty. They certainly weren't giving the death penalty to someone who halachicly didn't deserve it and had clearly done Teshuva