It makes sense to lease a vehicle for work if it will be used mostly for that work, you can bill extra for it, the amount of work justifies it, and you don't want to tie up too much of your capital. It's like renting office space - it makes sense if it generates extra income. Plus, there are neat tax write-offs for leases as opposed to financed or owned vehicles that help the decision making process. But, spending money for the sake of tax write-offs is faulty logic - it's still money that you won't have any more, so if you can avoid the expense, do so.
But, if it's only a side gig, just use your own car if it serves the purpose, and claim the mileage back as others have suggested. It will be cheaper.