Hey Sergey,
I actually reached out to Leaseplan about a year ago. The one in Portugal does speak english but barely fyi. So yes you would need a NIF and be a resident. You cannot do it as a foreigner. On top of that you would need a Portuguese bank account.
From some of my research you can find a cheaper deal going to a used car lot and getting a car minus the vat on a leaseplan type deal. Also you can go to your Portuguese Bank once you have it and they have lease financing plans.
For me it's cheaper to rent a car then Leaseplan or even buy a used car. The VAT is amazingly expensive and Portugal one of the most expensive places in Europe to buy. Keep that in mind as you shop around.