The preference for this sort of thing is a silicone rubber adhesive.
If you just want a little bead around the edge , then the standard acetic cure silastic like (silastic 732RTV ), e.g. window / aquarium adhesive is best. It's kind of translucent but looks clear in thin sections. The silicone is undamaged by sunlight and wont harm the plastic.
If you want a full area transparent join then use the two part silicon rubber that the DIY PV panel builders use. (Sylgard 184 or PV 6010 )
I would avoid any kind of solvent cure adhesive. It is possible to get some really good joints using specialty solvent adhesives, (e.g. acrifix) but can end in disaster unless you know exactly what you are doing.
Also avoid any anerobic adhesives (Loctite) , the vapors from these will cause crazing of the plastic.
Also be careful with cleaning solvents , only use water + trace of detergent or alcohol. Many of the hydrocarbon solvent cleaners will cause the plastic to craze.
Have you considered sandblasting the inside of the lid? It's difficult to get uniform, but saves the hassle of diffusers and gluing.