Knowing what idiots site monkeys can be, I would be inclined to have your house / neighbours house fully inspected ie a Periodic Inspection Report. This will reveal any anomilies with your system, and will include testing of the RCD. This may not reveal an actual cause of the issue, but at least you will know your system is good (or not). In my experience when you have a strange fault, you need to right back to basics and start from scratch.
You could also try something else first:-
1/ Switch off circuits controlled by RCD and ask neighbour to start lawn mower if it trips I would suspect RCD but still be concerned how its being affected by neighbours.
2/ As above but if RCD does not trip, turn on one circuit and start mower again. If rcd trips make note and repeat for other 3 circuits. If RCD only trips when one particular circuit is energised, then there is likely to be a fault with that circuit. If it trips across more than one circuit, then fault lies with RCD or something else in system.
Either way expect a good days head-scratching and much deep thought
You could also try something else first:-
1/ Switch off circuits controlled by RCD and ask neighbour to start lawn mower if it trips I would suspect RCD but still be concerned how its being affected by neighbours.
2/ As above but if RCD does not trip, turn on one circuit and start mower again. If rcd trips make note and repeat for other 3 circuits. If RCD only trips when one particular circuit is energised, then there is likely to be a fault with that circuit. If it trips across more than one circuit, then fault lies with RCD or something else in system.
Either way expect a good days head-scratching and much deep thought