Aldi 12V Cordless Mini Air Compressor

I have exactly one of these Roger, Lidl not Aldi, but same I think.
Couple of points...

It works very well, my tyres are all 60psi it manages that easily.
The trigger lock and preset max pressure are both good as its not fast!
On a full charge it will top up all 4 of mine from, just say, 55 to 60.
It also has a 12v direct input from a cigar lighter plug. This would work fine, but in most cases the cable wouldnt reach a rear tyre from the dash.
The main battery is mains charged, so either charge from EHU or, in our case a 300w inverter, only used while travelling.

Car and bike tyres, mine are 75psi, are no challenge to it.

All in all imho a better option than a wired compressor.

Wonder if my De Walt batteries will fit it, looks similar but ..... 

Virtual guarantee they won't. Only tool range with not only interchangeable batteries and good prices too are the Lidl ones

There's really no need to worry, the battery supplied, fully charged, will easily cope with any routine top up of all 5 wheels, we store ours fully charged or charge it from the inverter while driving. In that case it'd cope with a bigger leakage than just a top-up.
Let's face it if a tyre is flat you need the spare!! 
On that subject, we keep the spare at 60psi, same as the other 4 at all times, bad enough having to change to it far less changing then inflating!!