I thought it was because he wanted leverage, i.e. Without the Circle he is a nobody that the Senior Partners can easily get rid of. So he needs powers to be somebody they’d even care to have on their side. Lindsey was always a very -do things on his own terms - kind of guy.
Him leaving was never satisfying for me. Seemed like W&H would be able to find him wherever he went, whenever they wanted, either way
They might have mentioned that (I don't remember), but why would he need leverage? When he left town in S2, I don't think the Senior Partners were looking to kill him or get revenge on him. From all that we gathered in the early seasons, Lindsey was liked by the higher ups at W&H. They liked his morally grey character! I just never understood why the Senior Partners would be aiming to get rid of him. THAT IS, until he came back and screwed around with their plans for Angel. Which, again, makes no sense. If he wanted to be on W&H's side, then he would have helped Angel, no?
The only logical explanation I could ever muster on that front is that Lindsey had petty jealousy toward Angel. He hated the fact that such a moralistic, goody two-shoes vampire with a soul had taken over his spot at W&H. So he wanted to screw Angel over, even if it pissed off the Senior Partners, and hopefully find a way to still end up in the SPs' good graces.
Even with that said, though, I needed more information about Lindsey. How did he know about the amulet and did he go to Sunnydale to pick it up underground?! Like, what the hell! Was he tutored by some wizard on how to use glyphs and enhance his physical strength? It just feels like a character they should have explored more if they planned to bring him back. Like, we spent an entire episode on Harmony, which was funny enough, but why not spend more time on characters meaningful to the main plot?