Ok so he didn't want a war with the Lannisters... but he happily marries the girl implicated in the assassination of the King and wanted by the Queen Regent into his family. Kinda think pissing off the Lannister is inevitable at this point. Simply going ahead with this plan is an act against the Lannisters, end of story. I don't deny that it makes sense for Roose Bolton to seek out this marriage, only that by arranging it Littlefinger puts himself at great risk for a reward he could easily achieve after Stannis has been dispatched.
You're right, pissing off the Lannisters was an inevitable end to a necessary decision. But it isn't like Roose wrote a letter to Cersei telling her that he was done with her now that Sansa was part of the family. He just wanted a Stark heir, and probably would've handed Sansa over afterwards. That's feasibly negotiable, or at least something he could maybe delay through. If anything, the Boltons being the Boltons would've made that wait more tolerable for Cersei.
And even though he could after the battle, Littlefinger doesn't want to take Winterfell, he wants Winterfell to be given to him legitimately. That required pitting the Lannisters and Boltons against each other with Sansa. Taking Winterfell by force from a weakened House Bolton that wasn't harboring Sansa would just be rebellion. So sure --
-- he could've lied and probably possibly gotten away with the same thing, but at that point you don't have a story, you're just pulling stuff out of your ass. He might as well say the Boltons are conspiring with the Targaryens and Dany is arriving in Winterfell soon with 100,000 Dothraki.The exact same is true if he does send Sansa to Winterfell, which he does and Cersei doesn't follow up on at all. What if he sends Sansa to Winterfell and Cersei checks on it without telling Littlefinger, it's going to look pretty suspect when Roose starts namedropping Littlefinger for no good reason. That's to say nothing of Littlefinger misjudging Roose's loyalty to the Lannisters, exposing his hand too early with Sansa and implicating HIMSEFLF in Joffrey's death by harboring a fugitive from the Crown only for Roose to turn around and send Littlefinger's messages down to Cersei as a warning to her.
He "advises caution" with Cersei, telling her they should let Stannis and the Boltons fight and then take Winterfell from the weakened victor. Nothing about his plan actually requires Sansa to be inside Winterfell.
Sansa is in Winterfell. Littlefinger tells Cersei Sansa is in Winterfell. Cersei says 'Okay, Sansa is in Winterfell, so screw them'. We move on, because it's established. That we didn't see Cersei work her way through the fact-checking process or we didn't see an off-chance hypothetical isn't a red flag for shenanigans. I'm perfectly okay assuming that if Sansa wasn't in Winterfell then Cersei would find out, the same way that I'm confident that there are some sort of toilet-like devices in the Star Wars galaxy, even though I've never seen one there.
All of that is perfectly valid, if your goals are the same as Sansa's. Littlefinger's aren't. He doesn't want to join a rebellion, or make the North safe for Starks again, or take back Winterfell by force. He wants to be granted the North because he swooped in with 95% of the battle fought and tipped the scales in whatever direction would be most favorable to him, and Sansa doesn't have the leverage to make things otherwise.
What doesn't make "sense" is him ceding Winterfell to Sansa, Jon, and their negligible force after mopping up the Boltons. He was fulfilling the Lannister end of the plan, but didn't follow through. That's either due to bad writing, or to Sansa, and we won't know the deal with that until the show tells us.