Iguanas, like most reptiles (not all, I kno, I kno) are solitary animals.
Put yourself in the mind of a well-kept healthy captive reptile:
> you have your own food aplenty
> you have a reliable water source
> you have your own basking spot to enjoy without need of
protecting it
> you have no predators (taken the animal is now
socialized/tamed) or other animals to keep off your food.
Having said that, you can rest assured your iguana is fairly content in an ideal captive envirnonment. Now, we all now they would be much happier free in the rainforest, but since they got here, might as well keep 'em happy and healthy right?
Reptiles such as Solomon Skinks and others, that are social animals, are encouraged to be kept in groups. Anoles as well in "harem" types of conditions (so I've heard).
Of course, no animal can ever be happy without some stimuli....visual or audio.
Some people keep a small fish tank near the enclosures to give their iguanas some visual stimuli and something to watch.
Outdoor enclosures are the best because with birds flying/singing, winds, sounds, etc. the animal is exposed to a more natural situation. In-door things have to be setup so the animal does not go brain dead (admittedly it's a small brain, but nonetheless).
So a partner is not needed, but some interaction or stimulus with the outer world is indeed required for the animal to be "happier".
Regards,
-IJ