I always thought a Lord of Heart would function the same way as Hades, basically. As far as dream bubble creation, feferi made them as a witch of life so it doesn't take someone as powerful as a Lord or muse to make them. I bet a doom player could create a similar space, due to the fact that most deaths are in doomed time lines. Perhaps not a dream bubble, but something else! Don't forget that people can combine fraymotifs, and work together to make something cool, even if one of them is doom!

But see, the thing is, Feferi didn’t create the Bubbles. She convinced the Horrorterrors to Bubble them up for her- If you want to physically create them yourself, you need to be as powerful as a Horrorterror is, which are described as basically one of the few things in Homestuck that are close to true Omniscience and Omnipotence. So it’d take a little bit more effort.