Question

what need theory would explain why lemuel greene was unhappy despite his high income?

Answer 1

Well the possible theory will be of McClelland’s "theory of growth need". Which explains that income is not the criteria of a individual satisfaction with in a organization or company. 
This theory tells that satisfaction is actually depend on 1) power need
2)need for achievement and 3) need for affiliation.
in this case lemuel greene may be not satisfied with the power or with it's achievement and he wants to do go ahead and do much better than  that.

Answer 2

Answer:

This theory tells that the high income is not the correct criteria for the satisfaction of a person within a firm or organization

• This is why Lemuel greene was unhappy despite having the high income because either of lack of achievement need or power need or may be both of them.