This is a normal happening.
I open my BGE with intentions of cooking like Bobby Flay. I lift the dome to inspect how much lump I have inside. Slowly and ever so gently the dome starts to close. I lift it again and again and finally it stays. Coals loaded in and lighter is in place. Lid still eases down. I get the fire going and I shut the dome. No problem. 10 minutes later when the fire is hot and I'm ready to pull out the starter, I open the dome and it stays open with no issue.
So my question is this, is there a reason my dome won't stay open when the BGE is cold?