because both are OPTIMIZATION problems i.e. we are maximizing something or minimizing something.
In assembly line scheduling we want to 'minimize' the cost and assembly line scheduling problem is sister of multi stage garph problem.
In LCS we want maximum length of matching string sequence which is again can only be done effectively by dynamic programming . Remember these type of problems can lead to poor performance if we apply greedy algorithms (as all aspects are not known in greedy because we focus on currently what we have as min/max and we are not taking decisions at every step)