Most western saddles have a leather thong to hold the ropers lariat. I loop my lead rope and lash it on with that thong.
If you don't have one. Take a piece of leather tie, attach one end near the horn with a screw and concho, In the other end put a SLIT that is large enough to fit over the horn.
Coil the lead. Make 2-3 loops around the lead with your thong, and slip it over the horn. If my lead has a snap, I usually thread the thong thru the snap you help hold that extra weight
I don't know if it will show up in this resolution, but I have my black lead rope coiled and attached in that position, in front of my right knee
I also carry hobbles with me when I ride. Usually I thread them thru the ring where the back cinch attaches and just let them hang, Like a loose billet. But on pack horses where that ring doesn't exist or is hard to reach under the pack, I just loop the hobbles around the horses neck like a dog collar. That way, every horse has it's own hobble and I'm not looking for one when it's time to stop for lunch
Horses grazing on hobbles during lunch stop