Following journey across lake, promise to leave husband and travel widely (5-4)

'following journey' is the definition.
'globe trot' can be an answer for 'journey' (thesaurus). I'm not sure about the 'following' bit.

'across lake promise to leave husband and travel widely' is the wordplay.
I cannot really understand how this works, but
'lake' could be 'l' (geographical abbreviation) and 'l' is found in the answer.
'promise' could be 'bet' (betting is a kind of promising) and 'bet' is located in the answer.
'leave' could be 'go' (to go is to depart or leave) and 'go' is found within the leftover letters.
The remaining letters 'rot' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?