Does Jaime have authority over the remaining Lannister forces?

he doesn't. she's the queen. he rode north all by himself. not sure what he can do with just one hand but ya.

By all rights he should be lord of the Westerlands now that he's out of the Kingsguard, but if the queen wants to declare herself Lady of the Westerlands and general of it's armies, then the rightful Lord is out of luck.

He could follow the traditional path of settling disputes, calling on his allies to raise their troops and fight for him... But he's got no allies of his own.

He had authority only so long as he was following Cersei's wishes. She's the queen. She could countermand any order he gave, or relieve him of command as she sees fit. By leaving on his own he's basically resigned. I suppose he might try to take control of one of the Lannister armies in the field, by claiming Cersei sent him, but the moment they found out otherwise he'd be arrested. Unless of course he could actually convince them to switch sides. His sister may be in charge but she's not exactly popular.

That was an "it's about time" moment for me. When Lady Oleanna said that Cersei would get rid of him when she no longer needed him, I wondered when it would happen. She got herself pregnant so the Lannister name would continue and that's all she wants. I was hoping he would be able to bring others with him but it doesn't look like it.

If he survives I can see him going to Castely Rock and live there the rest of his life.

I think she lost him at "elephants fighting undead dragons"