I have read in Wikipedia and some other texts that
The halting problem is [...] decidable for linear bounded automata (LBAs) [and] deterministic machines with finite memory.
But earlier it is written that the halting problem is an undecidable problem and thus TM can't solve it! Since LBA are defined as a type of TM, should the same not hold for them?
The halting problem is solvable for any Turing machine which uses a known bounded amount of space, by a generalization of the argument given by Yonatan N. If the amount of space is $S$, the alphabet size is $A$, and the number of states is $Q$, then the number of possible configurations is $QSA^S$. If the machine halts then it must halt within $QSA^S$ steps, since otherwise, by the pigeonhole principle, it has a repeated configuration and so is stuck in an infinite loop. Therefore to determine whether the machine halts, we just run it for $QSA^S$ steps and see whether it halts within that time frame.
You seem stuck with a logical problem.
From the fact that there are books that you cannot read, you cannot infer that you cannot read any book.
Saying that the halting problem is undecidable for Turing Machines (TM) only means that there are machines for which there is no way to determine whether they halt or not by some uniform procedure that will always halt.
However there are Turing Machines that do halt. Now take a subset of Turing Machines, called the Nice Turing Machines (NTM), such that it contains only Turing Machines that do halt if and only if the tape contains an even number of symbols. If a machine M is known to be from that set, you have a simple way to decide whether M will halt: you check whether the number of tape symbols is even (it requires only two fingers).
But that procedure will not work for TM that are not in the NTM set. (too bad!)
So the halting problem is decidable for the NTM, but not for the TM in general, even though the NTM set is included in the TM set.
This is actually critical, and sometimes forgotten, when interpreting undecidability result.
It may well be that one can prove that an important property is undecidable for a very large family of mathematical or computational objects.
This does not mean that you should stop looking for a solution, but only that you will not find one for the whole family.
What you may then do is identify relevant subfamilies for which solving the problem remains important, and try to provide algorithms to decide whether the property holds for members of that smaller family.
Typically, halting is undecidable for TM in general, but it is decidable, often very simply, for large and useful families of automata, which can all be seen as special cases of TM.
In short, A LBA has finite number of configurations, say D. Hence, we can run for D steps and conclude the result. If it runs for more that D steps, by pigeonhole principle, we can say that, it is stuck in an infinite loop.
