Is your problem really that "our product doesn't use a framework"? Why is that an issue? What difference does it make?

Perhaps you feel that, using a framework, the team will be able to ship features faster, or get better performance, or higher code quality.

You'll be right. Sometimes. Frameworks have learning curves, and performance overhead, and maintenance costs. They're not always a positive gain.

And on the opposite side you see teams investing too much time on new tech, frameworks galore, instead of making progress to ship a working product.

As much as you feel your team leader is stuck in his ways, he may feel you're coming at him with a checklist of "hot shiny new tech" items you want to cross off, at the expense of delivering real value to customers.

So I suggest starting from the end, by looking at the outcome: are you building the right product? on time/budget? are customers happy? how's the quality?

And if the outcomes are off from where you expect them to be, start looking at what technology/people changes could help improve those outcomes.