Feasible? Sure, there are lattice algorithms that are competitive in performance with RSA.
However, there are drawbacks, like:
- They've been studied less than RSA or ECC, especially the individual algorithms.
- The most well studied system, NTRU, is patented.
- No generic proof that I know of that there isn't a quantum algorithm to solve them.
The first one is why I doubt TLS will quickly move to lattices at least unless there's significant evidence that a quantum computer capable of breaking current crypto is practical. The third means that even then another public key system might be better, if such can be found.