Your question seems to infer that both of the title characters in these plays are somehow stoic in the way that they respond to the tragedies that befall them. Let us remember that to be stoic is to respond to calamity by calmly carrying on with your life and not expressing emotion. This is something that both Lear and Hamlet definitely do not do.
Let us remind ourselves of how Lear greets being ejected from both of his daughters' homes at the beginning of Act III scene 2:
Blow, winds, and crack your cheeks! Rage, blow,
You cataracts and hurricanes, spout
Till you have drenched our steeples, drowned the cocks!
His sense of rage against his daughters and "ingrateful man" is plainly evident in his desire that the elements should take the revenge against his daughters that he is unable to take.
In the same way, Hamlet spends most of the play berating himself for his inability to act and raging against himself because others seem to have more passion and be more active than himself, whereas he feels he has more cause to be more passionate and more active. His indecisiveness is something that rouses him to attack himself fiercely. See his soliloquy at the end of Act II scene 2, when he calls himself a "rogue and peasant slave" because the Player is able to muster up more passion for Hecuba, somebody he has never met, than he can for his father.
Neither character is stoic in any way. However, when we consider the fate of these characters, perhaps we could argue that they would have been better off if they had responded to the tragedies they face with stoicism. It might have averted some of the calamites that befall them in their respective plays. This, however, is only conjecture.