Just returning to confirm my experience. As discussed above, Uber to AIFA (NLU) was not a problem and pretty fast at around 8AM on a Tuesday for a cost of under $500 MXN ($483 to be exact). There was an option to pre-arrange the return/pick up on the Uber app but I did not progress with it and when we landed, and tried to see if it was possible to book a trip from AIFA, the app was showing the message "no service available". So we took the transfer BUS to MEX (Terminal 1, outside Gate 7, which coincidently is one of the gates where Uber can pick you up), and then Uber back to the Hotel. Once again Global Adventurer thank you for your very valuable advice (I also followed your advice in other threads and stayed at the Sheraton Maria Isabela, which was indeed in a perfect location, preferred this to the FourPoints as price was very close, but this had a swimming pool, which we used).

With regards to lounges, we used the Sala Lounge Hacienda Santa Lucia, and the place was quite nice and quiet. There was a complimentary massage on offer but it was busy and although we had booked a session, we had to leave before our turn came up (They could have managed the booking better I believe). Food was ok, with an hot menu/table service where you could order one complimentary item, and the rest was buffet/self service style. Drinks were also complementary as far as I could gather (we did not have any alcohol as it was breakfast time for us).


edit (a day later): I have just received a notification from Uber (basically over a week after the trip) that the tariff for the above trip was amended so to add MXN 26.00 to pay for the toll road the driver took… not a massive difference, but nevertheless I thought it should have been quoted in the initial tariff.