Is secure lattice based cryptography in future?
With math and computational advances, for protecting systems we should increase key size. We know that recommended key size for lattice based systems such as the NTRU is approximately $3slog(s)+1000$ bit, which $s$ is a desired security level.Today $s=80$, but with the advances of math, $s$ is increasing. $s=96$ is believed to provide protection until $2020$. So if we use lattice in future we should increase its dimensions.

For more detail about other cryptographic Schemes complexity you can see "Cryptographic Schemes
Based on Isogenies" and also 
"Yearly report on algorithms and key sizes".