L just let her cry, feeling the dampness from her tears and her running nose seep through his shirt. It was not the most pleasant of feelings, but he allowed it for not knowing anything better to do. If it helped to comfort Rachel then it was for the best. He was not going to deny her a place to cry.
When she stopped and mentioned his shirt he decided to take a look and see what the damage was. Upon inspection L determined that the shirt wasn’t exactly ruined, but it definitely had to be washed.
“I have spares where I am currently staying,” He assured her. He could always change when he got back to the place he had been staying, or he could go back to Asgard for a while to be closer to her. This of course, being if she wanted him to.