We do "hover" lunges using a TRX that you could certainly try using a sturdy piece of furniture or ballet bar or something else at home. holding the TRX handles we lunge back and down, just like a normal lunge except the back foot never touches the floor, the shin is parallel to the floor. Obviously this is different than your traditional lunge because all the work is in the front leg but certainly better than no lunge option at all.
Also, we worked on a pose in yoga class recently that was like a crescent lunge but the back foot was pointed, top of the foot down on the mat. This was a lot of work for the hip flexor on that back leg. Not sure if that kind of pointing the toe would be problematic based on what you described.
Hope this is helpful!