You can actually hear the lyrics of the theme song in the episode "Lucy's Last Birthday". This is the only episode to broadcast it in full!

The lyrics are: "I love Lucy and she loves me. We're as happy as two can be. Sometimes we quarrel but then. How we love making up again. Lucy kisses like no one can. She's my missus and I'm her man. And life is heaven you see. 'Cause I love Lucy, Yes I love Lucy and Lucy loves me. (I love Lucy and she loves me. We are as happy as two people can be. Sometimes we quarrel but then what do we like about our reunion. Lucy kisses like no one else because it's Lucy I love, yes I love Lucy and Lucy loves me).