I typically roleplay my favourite summon, Mr. Great Lizard, as being possessed of a keen intelligence, capable of understand the subtle nuances of human speech. How wrong am I to be doing that? Keeping in mind it's a spell from the goddess of intelligent beasts so I think it's not so much of a stretch, but...

It summons an actual normal creature of the type, erm, summoned. So, it wouldn't know words and such in the case of a lizard.

You are able to magically command it to do your bidding, assuming the command is extremely simple, and physically possible for the creature.

Even if it's Greater, in the case of the Greater Stone Lizard, Mr. Great Lizard?

Yes, it would be a bigger lizard.