Unfortunately I haven't done Oasis yet, but all ships post the dinner menu at the dining rooms after lunch so you can see what they serve the same day.
They usually have a rotation of menus so it's unlikely you can predict what will be the next day. Usually lobster is on one of the dress up nights, I would ask your server on the first day when they think it will be they might know or can ask.
Spa tours can be done anytime just ask to have one and they will show you around. The giveaway is on the first day usually around 5pm right after boat drill. Check your itinerary for exact times and don't be late. If you miss it they have daily specials usually cheapest days to go are when you in port or on the last day.
Have fun and blow all your budget in the spa.