It's not a wonderful idea to use it without a lid. Because the hot tank is below, it will get warm between uses and will eventually have stuff growing in it (rarely nasty, but annoying all the same).
There are any number of things you can use as a lid. one of the easiest is probably just a flat piece of polystyrene. This will help prevent it freezing in the winter.
You could also use plywood and pin a bit of polythene (strong bin bag?) to the underside (fold it up over the edges and pin on the top surface).
There is most probably an expansion pipe too. This goes up from the tank below and points down into the upper tank from above. It allows the hot water and air in the system somewhere to escape to, when the tank below warms up and the water/air expands. If there is one, you will need a hole in the lid for it too. If it's awkward (small ones are worse than bigger tanks), split the lid into two parts, so that the hole for the pipe is on the line of the split.
Also, most builders' merchants sell 'collapsible tanks'. These are circular and made of thin walled plastic (and they come with lids!), They're designed to fit through small openings: you warm them up, with a hot-air gun (be careful) or a fan heater, then scrunch them up through the loft hatch (or into the cupboard in your case), then let them return to their original shape.
Check to see if they do one small enough for your situation. If so, that's probably the best solution of all, but don't cut the old one up until you know you can replace it!
Final thought: at a guess from your picture, the shelf the tank is standing on would come out easily. If so, you don't need a collapsible one - any ordinary small tank could replace it from below (then fit the shelf back underneath the tank).
Hope something above helps!
E.
Hi im very new to the internet 
