Over time, as adults, we develop coping mechanisms, strategies, action plans, for dealing with our own shit. Either we get pretty good at it, or we don't. When we're not very good at maintaining our own emotional boundaries, things begin to come out sideways.
It is not our job to fix broken relationships or broken people. Our job is to show up in the arena of a relationship and do the best we possibly can to love and be loved.
You must give your partner the assurance that you are not running away. And you must also allow them to hold their own pain. By "staying in your own lane" you are giving them several strong messages.
By allowing you to experience and process your own distress, without my interference, I am giving you the utmost respect. I am viewing you as whole, strong, and capable. And in my affirmation of you and your inherent ability to be strong and sufficient, I am reaffirming my belief in you.