With some luck, you'll see an eagle on the Lake (7)
I believe the answer is:
lucerne
'lake' is the definition.
(Swiss lake)
'with some luck you'll see an eagle on' is the wordplay.
'with some luck you'll' becomes 'luc' (I am not sure about this - if you are sure you should believe this answer much more).
'see an eagle' becomes 'erne' (erne is a kind of eagle).
'on' is a charade indicator (letters next to each other).
'luc'+'erne'='LUCERNE'
'the' acts as a link.
Can you help me to learn more?
(Other definitions for lucerne that I've seen before include "Fodder plant - lake" , "Clover-like plant used for fodder" , "Alfalfa - Swiss lake and resort" , "Food for cattle" , "edible plant" .)