My mower needs to be mounted on a tractor, so I wouldn't lend it, except to one person who always takes great care of borrowed machinery and sends it back in better condition than they got it. I don't have a lawn any more, but I have a strimmer which I use for between the vegetable beds and that sort of thing. It cost a lot of money and is easily damaged, so I might lend that out, but I'd be really careful who to. The person most likely to ask is my nephew, who is lovely but an absolute calamity with anything mechanical. I would lend him the strimmer, but insist I also lent the operator!
Has the mower been serviced yet? How expensive and easily damaged is it? Does the neighbour usually speak to you, or do they ignore you? Do they have form for damaging or not returning things? Are you likely to need a favour from them? I might wonder how long the "process" of getting a new mower might take - surely that's a fairly quick job unless finances mean that you might not get the mower back before you need it.
Actually, I've just remembered the last time I lent a mower to anyone, and I've changed my opinion. My father borrowed a cheap hover mower which I had used my last money to buy (I was broke largely because a condition of my relationship with my parents was working for them for nothing). He used the mower, then refused to return it. After a month or so, he left it out in the rain and yelled at me because my mower was crap and had stopped working (this was after I had brought up the subject of maybe needing it back at some point).
I'm not sure if I think that lending a mower is a bad idea, or just that having abusive, violent parents is best avoided. It's been a long week and it's only Tuesday! Perhaps lend it unless this is the first time they have bothered to speak to you, or say "No need, I'll do it for you" so you know it will return.