How well a tent works for solo hiker plus dog depends on several things, one of which is the size of the pup.
My dog, mostly Lab, is 80 lbs. He doesn't take up a lot of space while sleeping because he curls up in a ball on his 20" x 30" pad, but he close to doubles the amount of air exhaled into the tent. That means that a solo tent designed to ventilate for one person may have serious condensation problems when the dog is added. My experience is with a SMD Lunar Solo a few years ago. In good weather, when we were only in the tent to sleep, with everything wide open, it was fine. My dog just fit in the triangle at the back. When we were confined to the tent by rain for several hours before bedtime, though, it was too cramped. The dog needed more room and so did I! With the vestibule partly closed on wet nights, condensation was a major problem. The one good thing was that I could sit up while still in my sleeping bag, and wipe down all the walls. This worked out fine if I could get it done before my dog woke up and went into his morning tail-wag routine!
I suspect the Lightheart Solo would work fine (maybe not with a St. Bernard or Newfie, though!) when it can be wide open, but if it has to be closed down in rainy weather, that might be another story. I've never seen one so can't comment.
EDIT, later: I'm wondering if the porch or awning version would be better ventilated in wet weather? This might be something to take up with the Lightheart folks?
Back to the bivy/no bivy under a tarp issue: I'd love to switch to a tarp, mainly for the views, but don't see much point if I can't save weight while doing so. Of course I don't want to get wet, either!