Complements of Linear Bounded Automata?
It depends whether the automaton is deterministic or not. If it is deterministic, then the answer should be yes, just as in the case of DFAs, and you can mimic the proof for DFAs. If it is non-deterministic, then the answer should be no, just as in the case of NFAs; in fact NFAs are a special case of non-deterministic LBAs, and the NFA counterexample can be adapted to the LBA setting.

(The set of languages accepted by non-deterministic LBAs is closed under complementation, but the proof is not quite as straightforward; it is known as the Immerman--Szelepcsényi theorem.)