I'm wondering if this is possible or if there is some schedule conflict between some side quests.
To answer the original question and the edit at the same time:
No, it is impossible.
To get the All-Night mask at the Curiosity Shop, you must save the old lady in North Clock Town on the first night. This causes Sakon not to visit the Curiosity Shop, stopping the Kafei-Anju quest, meaning you cannot get the Keaton mask, or the Lover's mask.
This walk through of the Kafei and Anju side-quest states it can be completed in two different ways, one of which gives a bottle, the other the postmans hat:
Remember that letter that the Curiosity Shop man gave to you? Well, it needs to be delivered to Madame Aroma. You can either hand deliver the letter to Aroma (you’ll need the Romani Mask for this), or you can hand the letter to the frantic postman at the post office. If you choose to deliver the letter to Aroma yourself, [...] she’ll reward you with a new bottle that’s full of Chateau Romani. If you take the other route and give the letter to the postman, [...] talk to him to receive the postman’s hat.
The lottery isn't a sidequest, really, since ever doing it isn't logged anywhere. You need to do at least 2 cycles to fully complete all sidequests.
However, it is possible to beat the game itself (ignoring all sidequests) in just one cycle (after the initial 3 days needed to get your Ocarina and human self back, of course).