Create a cycle path on the pavement or make it shared use, from after the bus stop in Liberton Road around the corner to the junction Gordon Terrace/Esslemont Rd.
This would allow cyclists who want to turn left from Liberton Rd towards KB to bypass the traffic lights, then continue onto Gordon terrace or rejoin the other traffic in Esslemont Rd.
Currently it's dangerous because:
(1) this route is uphills and cyclists are going slow, but cars turning left can't see ahead if there are cyclists.
(2) cyclists have to wait at the light and then are in front of cars, so drivers get quite annoyed having to trundle along until safe overtaking is possible in Esslemont Rd, many attempt dangerous overtakes earlier. If cyclists can bypass the red lights they have a chance to go up the difficult bit during quieter phases
(3) cyclists who are not in the ASL (but also those in the ASL) are in danger of being left-hooked (see also http://edinburgh.cyclescape.org/issues/1532-segregate-the-feeder-lane)