This boils down to a case of subject/verb agreement.
As a quick reminder, singular subjects require singular verbs, and plural subjects require plural verbs.
Expectation is singular, expectations is plural. Whichever you choose needs to have the appropriate matching verb to go with it in the 2nd half of the sentence.
However, in your sample sentence, you're given a clue. It says "...that Lewis Hamilton
IS under..." 'Is' is a singular verb, which tells you that you need a singular subject, 'expectation'.
So, "The expectation that Lewis Hamilton is under is causing him immense problems."
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