I don't think that laziness makes things much harder. Compare a C function with if foo return 0 in the middle and a Haskell function that lazily builds thunks that don't end up being evaluated in a particular branch. There's obvious things to do to both to make them run in constant time. The hard part about dealing with a timing attack in both cases is recognising that the function is used in such a context and needs to be constant time.
AFAIK, the haskell TLS stack has not yet been audited. For this reason, there's some reluctance to use it in parts of the Haskell community. Although http-conduit and http-client-tls do use it, so everyone writing programs that hit https from haskell using conduit is using it already.