LY is NOT done at 45 degrees (because they would hit themselves behind because there is NO bend)...but about 35, or at the beginning even less. The horse should remain straight through the body and only minimally flexed (away from direction of travel). Head to the wall, for a few steps, pulse/relax/pulse/relax is the traditional way of doing it/coordinating leg/rein and then immediately straightening. Why? Because the rein away from the wall is more easily met, but if you are too strong the horse will slow, stop, even start a turn on the forehand. All of which could be intentional exercises. Since it is not a traditional (srs) exercise because it has no bend it used to be used very little (suppling but not engaging). With a Swedish team coach in the 60s it was added to event, and later dressage, tests. So many use the exercise whether it is a good idea or not for a particular horse, and this could be imbalancing. A good use of this exercise is for a horse which tends to go too low/btv, it will change that for the better.
Another way of teaching the horse the same reaction (move from inside leg), is to do spiral circles, starting at a and 'drifting' on the open side toward c until the circle reaches c progressively. As you leave the wall, think en-large. This means two pulses coordinated with the movement of the inside hindleg. Then 3/4 of a circle ridden as a normal circle. The good part of this is that there IS a degree of bend, and the horse 'falls lightly' into contact with the outside rein more than in a traditional ly. It is a better way to 'connect the horse to the outside rein's limitations.
The other way is to ride onto the inside track or 3/4 line, and then flex lightly to the inside and then touch with inside leg (again it HAS to be coordinated with the inside hind leg). It is not pull inside, throw away outside or the shoulder will pop. RIder looks where horse looks (straight ahead, slightly away from travel line). Horse is parallel to longside wall ( It is a very gradual line, not 45 degrees as a half diagonal would be for a GP horse's half pass).