My phone is lost and I hadn't backed up any of my most recent photos. If i pay for more storage (remotely), will that give me access to all my most recent photos?

I wont give you a definitive no.

but it is very unlikely.

To the point that I would say, no it is not possible.

All these things would need to be true:

1. The phone must be turned on.
2. The reason it has not backed up or synced photos before is because of not enough storage.
3. iCloud photos, or iCloud backup needs to already be turned on on your device.
4. It needs to be connected to Wifi(or be setup to backup on cellular)
5. Have enough power to backup(will generally only do this when plugged in)