Lynn has a high pain tolerance. That's not to say she is unbothered by certain degrees of it or doesn't feel it until a certain point but she deals with injuries quite well, often laughing it off unless it's something severe. Lynn also tends to neglect injuries she does sustain. In this panel Lynn has suffered a hard hit (And it hurts like hell) But instead of reacting to the pain she lashes out of anger at the fact Junpei got hurt, instinctively craddling his body in a comforting/ defensive manner to protect him. While inhabiting Junpei's body Lynn isn't so reckless and is tentative of Junpei's wounds- because they are his.
She also wasn't begging for mercy. She was TELLING Mahito to stop hurting Junpei.