EDF and LST algorithms are not optimal if preemption is not allowed or there is more thhan one processor .Consider the following 3 independent non-preemptable jobs, J1, J2, J3, with release times 0, 2, 4 and execution times 3, 6, 4, and deadlines 10, 14, 12 respectively.

Both EDF and LST would produce the infeasible schedule shown in fig (a) Whereas a feasible schedule is possible fig (b) but left the idle period.

Consider we have two processors and three jobs J1, J2, J3, with execution times 1, 1, 5 and deadlines 1, 2, 5 respectively.  All with release time 0.

Then EDF gives the infeasible schedule (a) whereas LST gives a feasible schedule (b) but in general LST is also non-optimal for multiprocessors.

Hence both EDF and LST are not optimal in case of jobs non preemptive constrain and multiprocessor environment.