Since the Lightning network is a specific protocol and both implementations are open source and meet the specifications, it should theoretically Be possible to migrate from one implementation to another.
but nevertheless practically spoken will need a software tool that transforms all internal data formats of
lnd to those used in
c-lightning without altering the state of the nodes. I don't know any tool that converts internal data formats. That said, or you go out and create that tool or you will have to install a new node (even with a new nodeid)