A) Did they lie in the sun for half an hour?
b) Did they lie in the sun for half an hour or for an hour?
c) They lay in the sun for half an hour, didn't they?
d) (For) how long did they lie in the sun?
e) Who lay in the sun for half an hour?
(В этом предложении я бы, конечно, использовала Perfect Progressive. Но, раз уж оно Вам дано в Past Simple, то придется "работать" с этим временем)