There are definitely no lawns in the city, but usually houses will have a little yard-like area even if it's just for parking bicycles. Land is expensive, so it's a bit of a waste to put a lawn where you could have a larger room if you've bought the land at current prices. Older family houses will definitely have lawns, often complete with a little family shrine.

There are plenty of giant residential towers and more going up all the time.

The difference there is that there are laws that protect rights to sunlight, so it's difficult to build taller buildings in an established neighborhood: https://www.japantimes.co.jp/community/2014/08/24/how-tos/ne...