The different usage of "whatever" and "what"

Solution 1:

Whatever a man lacks in himself he will seek outside.

What a man already possesses in himself he will not bother to look for outside.

The clauses starting with "whatever" and "what" above function as topicalized direct objects, that is, as direct objects that have been placed in front position for emphasis. Without such emphasis, this is how the sentences would read:

A man will seek outside whatever he lacks in himself.

A man will not bother to look outside for what he already possesses in himself.

Therefore, using "it" after "seek" or "look for" would be grammatically incorrect, as it would entail a repetition of the object. However, some speakers may be found to duplicate the object:

? Whatever a man lacks in himself he will seek it outside.

? What a man already possesses in himself he will not bother to look for it outside.