Do you happen to know (even if just testnet) examples of such opening and closing/settle transactions?
Here's mine in testnet where I'm depositing 0.15 tBTC to a lightning node:
e8cbe013f7f5f4087aaf729b9b7eae79f5aabddb188ce4cc562cdb2a591251f8.
Isn't there any special bitcoin script placed in those transactions? So its a simple 2of2 output?
AFAIK, it's a simple 2-of-2. You can't distinguish a settle transaction from a simple one where you send funds to a 2-of-2 multi-sig address.