There can be a sexual energy connected with the balance forward in the lower abdomen; Kegels with the pubo-coccygeus would be connected with that.
I stretch both legs, first one then the other; I just wait until I can grab my toes and then ease a stretch on the hamstring until I feel I can breathe. I suspect it’s years of half-lotus on both sides that now enables me to get into the lotus, but there are specific coordinations that I call to mind to stay in the lotus and relax. The hamstrings and the quads reciprocate activity out of stretch, and that puts a stretch on the ilio-tibial tract. Stretch in the tract generates activity in the sartorius muscles that pivots the pelvis on the hips, left and right; with that pivot and stretch in the ilio-tibial tract, activity will be generated in the gluts that also pivots the pelvis left and right on the hips. Not volitive activity, activity generated by the stretch of ligaments and fascia that translates into different motions.