Hi FLL
The problem with trying to book lower end accomm in advance is:
1. finding contact details for the place. Many do not have websites. Some don't take bookings.
2. locking yourself into a particular accom or area when sometimes being flexible is a better option.
3. you may arrive and decide it is not what you are wanting at all, or hear about a fantastic place during your travels.
4. some may try to get a deposit from you, and they don't take credit card - or you wouldn't trust them with your card in advance anyway, so you are faced with trying to transfer money.
Of course, if you don't book you then run the risk of a place being full. However, this doesn't happen all that often unless you are travelling in peak season to very popular destinations.
Personally, I don't book well ahead. However, if I know I want to stay at a particular place 2-4 days out I will phone them and let them know I am coming. If you get something like Lonely Planet, it often provides the phone number of budget accommodations.
I can't comment on the Perama tour - perhaps ask on Thorn Tree Indonesia branch?
One place that is bungalow on the beach type accommodation that does take bookings in Mangsit (near Senggigi) is
Santai Beach Inn.
Also, Mimpi Manis in Kuta Lombok (who own this website) take bookings - I'm sure Gemma will respond with details.
You may find some accom booked out on Gili T in May, but there are usually alternatives - and you can always go to one of the other islands.