Are quantum preimage attacks on hash-based random oracles serious for lattice signatures?
Yes, it is important.  In a lattice-based Fiat-Shamir signature scheme, the signature is (z,c) where z is a low-norm vector and c is a low-norm challenge.  

The verification equation then satisfies c=H(Az-tc,m) where A and t are the public key (A is a matrix and t is a vector) and m is the message.  If the Adversary is able to find an m' such that c=H(Az-tc,m'), then (z,c) is also a signature for m'.  Thus having 128-bit classical pre-image resistance is not enough.