If the Lavellan Inquisitor was burnt alive... Would Solas walk into to pyre to share her fate...
Me? I think... YES.
Oh gods!
I can't think about this because, honestly, if he hadn't yet finished his mission, I don't think he would. His duty to The People would have to come first.
As much as he loves her, he's not going to throw away all hope for his people just to burn at her side. I think he'd try to save her. But if there was no hope for that then… no. He'd just have to stand by and watch her die.
If this hypothetical situation were to occur after he's completed his task, then… I think he just might. All these years he's been living just for the opportunity to right his mistakes, with that done he may finally be free to have a life, make choices based on what he wanted rather than what The People needed. He'd be free to die, if he so chose.