TAP question - two flight reservations, same day
 

We've booked a one-way business class flight with a stopover in Lisbon such that we're flying LHR-LIS one day and then five days later LIS-ORD. We're looking to book a trip out of LIS to RAK (Marrakech) upon our LHR-LIS arrival with 3 hours in between flights. Second leg will be booked in economy

Will TAP allow us to check bags LHR-LIS-RAK on two separately booked itineraries? Many US-based airlines would accomodate that? If not, I'm going to push the family to do carry-on only as I think claiming bags and rechecking would add excessive stress on a 3 hour "connection".

I'd stay on the safe side and avoid checking any luggage, especially if not travelling alone.

Unless you can hear it from TAP (and even then, you will be at an outstation so there is that to contend with) I'd assume you cannot check right through on seperate tickets.

I'd not trust TP's word on this. They often provide wrong information* and in this case it could have nasty/expensive consequences (missed connection and no rebooking on separate tickets).

​​​​​​​*A while back I had written confirmation from TP that my stroller would be delivered at the gate at LHR. Alas, it was not.

Short answer: no. If everything is on-time, 3 hours should be enough to re-check.
With Carry-on only, it's a very easy connection - just a simple security check. Alas, there's no lounge in the non-schengen area, so you may want to go through passport control anyway to get to the lounge.