It seems you are mixing two concepts in your question.
1.) the necessity of having an invoice
2.) the necessity of being online
Re1: invoices are not necessary with the not standardized keysend feature or the soon to be standardized BOLT 12 offers. Offers are specifically designed having refunds in mind as the also provide anonymous payer proofs which currently in lightning do not exist
Re2: both techniques in 1 still require both nodes to be online at the time a payment / refund is being conducted. That is just the nature of the protocol and there seems to be little we can do about it.