"I have had the same problem with L: her being so open, but I’m not in the position to give care. And to also not know whether to be completely open or not about my feelings when she is going through something difficult"

Yes, exactly this. Knowing on a logical level that this is my session, she wouldn't be here if she didn't want to be etc, etc...... and yet still feeling as though I need to tread lightly, maybe avoid certain topics. Probably all in my imagination, yet that's how I feel.