I recommend to print the tray upside down, without support. The lids will need support because of the hinges, and if your bed adhesion is less than perfect, you probably want to use a raft,. The Prusa i3 mk3's smooth PEI build plate gives excellent surface finish, but I had to tweak live Z and temperature to get it right.
For the lids use no fan, 0.2 mm layers, heated bed at 45 deg C for the first layer and 40 deg C for the rest. Keep hot end as cool as possible, I'm printing at 193 deg C (first layer 200). PETG might work better than PLA because its adhesion is even better.
I'm changing the lids a little so the hinges don't stick out that much and so are easier to print.
You can install the lids on the box by simply pressing them in. When your PLA is rigid, it helps a lot if you do it in a warm room or over the heater. In cold air the hinges might break while installing.