I was just in LIS a few weeks ago, and I definitely think it ticks every single one of your boxes. And it's the kind of place that can be as cheap or expensive as you wish to make it. There are plenty of mid- to high-end bars and restaurants (still very modestly priced in comparison to the US though), but just as many dirt cheap, hole-in-the-wall local gems.
Since it sounds like you're into cafes with old world charm - don't miss
Confeitaria Nacional when you're there.