Why???

Late reply, but as much as he wanted Sally and was attracted to her, he knew that she would eventually leave him, she was much younger and not with him for the right reasons. In the end, he knew he was better suited to a woman his age, who was "into" his past and his persona of being a tough guy. And she was previously married to a tough guy, which made them people of similar history. The "older woman" was proud to be with him and he sought that in people, to be admired and looked up to. Grace filled his needs in that way. Plus she could support him financially, something else he needed.

Because he sees that Sally doesn’t want to be with him. She took his money and quickly went out for “breakfast” in order to leave him. If she doesn’t want to be with him, then what is he supposed to do?

And all in all, I think his heart was really with Grace more than Sally. Why did he call Grace early in the morning to tell her that he killed those tough gangsters? He wanted to impress Grace. If Sally was his #1 sweetheart, then he wouldn’t have called Grace. Plus - Sally wasn’t impressed with the way Lou killed those gangsters, but Grace was impressed. That detail shows that Grace’s personality better aligned with Lou’s personality.

The whole movie appeared to be about his relationship with Sally. But it really wasn’t. It was about Burt Lancaster’s redemption. He lived as a low-ranking cowardly gangster his whole life. Killing those gangsters gave him one last chance to make up for it.