You can simply send a query to the Oracle on-chain Oracles only operate on-chain and you can send a query request to it on-chain and still use its answer off-chain. This is already implemented and is working with channels. What is more: you can already have a dispute about it.
Ex. Alice and Bob have a state channel. They are into football games and are gambilng for a certain game. They have a smart contract inside their channel and if Alice’s team wins - Alice takes the reward stored in the contract, otherwise - Bob gets it. Inside the contract itself there is stored the specific OracleId that they both agreed is the source of truth. This could be a set of oracles and we could build a consesus around their answers, but out of simplicity let’s have it a single oracle called Oliver So if Oliver states on-chain a certain result - Alice use his response to call the smart contract she has with Bob off-chain and claim her reward. If Bob is missing or somehow unhappy with the state of events, Alice can take this same off-chain smart contract and Oliver’s response with the result and execute the contract call on-chain and finally get her reward. This is all in place at the moment and is working in a trustless manner.
Then it comes the question who pays the fees required by Oliver for his answer. Obviously it is the one that calls it and if this is fair might not have a simple answer but since the off-chain smart contract can reffer to on-chain persisted data - for example oracle queries - they can have a special function handling that: if Alice asks Oliver for the match results once, she can claim the fees from the smart contract they have off-chain. In this way they could split the fees in any way they see fair and that’s the whole point of it.
If your question was more regarding some bridging service connecting on-chain and off-chain worlds (and for example calling oracles) - we still don’t have something like that. We already have all the on-chain infrastructure it would need, though: for example if Sarah is providing this service - she can ask Oliver (instead of Alice) and Alice still can use Oliver’s response in her off-chain contract with Bob. This can be greatly improved with virtual channels, but at the current moment Alice can have a state channel with Sarah and a contract saying hey, Sarah, if you ask Oliver THIS from my behalf, I will pay you the fees and some more tokens for the service.
So at the moment Alice can use Sarah to call Oliver in a secret and private way and can still use his on-chain response with her contract with Bob and then they can split the fees in some fair manner. What is even better is all of this is completely trustless. If all Oliver’s responses must always be on-chain is a matter of another discussion (hint: no, Oliver can sign messages to Alice, so she can use them in her contract with Bob).
But I agree there are ton of detailes yet to be polished. We all work in that direction.