Have you ever had a guitar in your hand, and you were sorta half asleep, but playing some pretty cool stuff?
(I'm pretty sure I actually fell asleep with my guitar in hand one time - but that's a different story). In the pic on the right, Bruce Springsteen clearly fell asleep...
Laid back blues - the cool thing is, you can basically use the exact same guitar licks you might normally use in a blues-rock solo, you know, faster, punchier licks... you can use those exact same licks, same fingering, same patterns, everything the same except how fast you play them.
And they'll sound GREAT.
There's no law that says you have to play a particular lick in any certain way.
So, if you want laid back blues, you play the lick that much slower, and voila presto, you've got it.
The great thing about blues licks like this is that for someone new to soloing, these kind of licks are exactly the right place to get started.
Once you're comfortable playing them "laid back" style, then by all means, pick it up a little and rock it out a bit more...
But start with the slower, laid back ones, and you'll not only learn quicker, you'll have a ton of fun and sound great doing it.