The phase diagram of 2d Lorentzian quantum gravity (LQG) coupled to conform
al matter is studied. A phase transition is observed at c = c(crit) (1/2 <
c(crit) < 4) which can be thought of as the analogue of the c = 1 barrier o
f Euclidean quantum gravity (EQG). The non-trivial properties of the quantu
m geometry are discussed.