Why Linear bounded automata requires Nondeterministic Turing machine ? Why not Deterministic Turing machine?
The conversion from nondeterministic Turing machine to deterministic Turing machines doesn't conserve space. The best known construction, known as Savitch's theorem, converts a nondeterministic Turing machine using space $s(n)$ to a deterministic one using space $O(s(n)^2)$, and this is suspected to be tight in general; see for example this question on cstheory.
Linear-bounded automata correspond to a class of grammars, context-sensitive grammars, in the following strong sense: a language can be described by a context-sensitive grammar iff it is accepted by some linear-bounded automaton. We only know how to prove this result if the linear-bounded automata are allowed to be nondeterministic. Indeed, assuming that $\mathsf{DSPACE}(n) \neq \mathsf{NSPACE}(n)$ (a conjecture which is much weaker than the tightness of Savitch's theorem), there exists a context-sensitive language which cannot be decided by a deterministic linear-bounded automaton.