Lasagne's first put into family oven (4)
I believe the answer is:
kiln
'oven' is the definition.
(kiln is a kind of oven)
'lasagne's first put into family' is the wordplay.
'lasagne's first' becomes 'l' (kst letter of 'lasagne').
'put into' means one lot of letters goes inside another.
'family' becomes 'kin' (synonyms).
'l' placed inside 'kin' is 'KILN'.
(Other definitions for kiln that I've seen before include "Large oven for baking pottery" , "Industrial oven" , "Oven for burning lime" , "Baker" , "Potter's Friend" .)