Icehouse has a big toilet with no lid (5)
I believe the answer is:
igloo
'icehouse' is the definition.
(house made from ice)
'a big toilet with no lid' is the wordplay.
'toilet' becomes 'loo' (loo can informally mean a toilet).
'with no lid' means to remove the first letter (in a down clue, lid could mean the top letter).
'big'+'loo'='bigloo'
'bigloo' with its first letter taken off is 'IGLOO'.
'has' is the link.
(Other definitions for igloo that I've seen before include "Living quarters" , "Eskimo's home" , "Inuit's home" , "Dome-shaped Eskimo house" , "Traditional Inuit house" .)