Getting the cover back on, lady, is the problem (7)
I believe the answer is:
dilemma
'the problem' is the definition.
(a dilemma is a problem)
'getting the cover back on lady' is the wordplay.
I cannot quite see how this works, but
'cover' could be 'lemma' (lemma is a kind of cover) and 'lemma' is found in the answer.
'lady' could be 'di' and 'di' is present in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'is' acts as a link.
Can you help me to learn more?
(Other definitions for dilemma that I've seen before include "difficult question" , "I lammed away to find perplexing situation" , "a problem for Shaw's doctor" , "Awkward situation" , "embarrassment" .)