Best option is take bus from lht to isl by daewoo.
From there u take riksaw or taxi and to go faizabad bus adda (some people say its skyways adda). From there u can take skyways bus to mazafarabad. They have coasters service for muzafarabad.
If I am not wrong so there 1st bus leave at 6am ot 630 am.
I am talking about summer, now its winter and sunrise late so chk the timmings again before travelling.
Approx travel time 3.5-4hrs
U can searcb google for their contact no. To confirm bus timmings