Hi Thomas,
The qutip.lattice module needs a fair bit of work. At the moment it does not support time-dependent intra-cell hamiltonians (as far as I can see) and I don't think it supports dissipative systems / Liouvillians either. Adding support for those might be a fair bit of work, but also an exciting project.
If you are particularly keen, we have split out the lattice module into a separate repository (
https://github.com/qutip/qutip-lattice) for QuTiP 5, and if you (or someone else) would like to clean up the module and broaden the system it supports, I would be happy to give guidance, review PRs, etc.
If not, it will likely get an upgrade eventually -- it's just not at the top of the list of things being worked on by anyone else right now (again, as far as I know).
Regards,
Simon