I agree with you, although I suspect my BE ear is informing me.
To my mind, the construction "Let's go [do something]" is either rather American, or plain unidiomatic, but it does depend on what the activity is.
In this context, I would say "Let's go karaoke-singing this weekend!" This is by analogy with with "carol-singing". "We're going carol-singing on Christmas Eve so we can't come to your party until late in the evening". There are many other activities which are suited to this construction in a simliar context.