Lyric discussion by madshell 

Cover art for 3 Legs lyrics by Paul McCartney

I agree with JDeanB here. The lyric "Well when I thought, well I thought when I thought you was my friend" could possibly be referring to Lennon in the context of Beatle history. RAM was an album full of angst and little jibes toward the broken relations of the four lads from Liverpool. I never understood the dog reference, but it sounds like defensive bragging.

I think the dog is The Beatles. With just 3 legs now(John, George and Ringo). It's very sarcastic.