The way I lubricate my nose when it's dry is to put some Vaseline or Petroleum Jelly inside my nostrils.
The Petroleum Jelly helps to keep moisture inside your nose and prevents nosebleeds in dry air.
You can also lubricate your nose by putting some coconut oil inside your nostrils which also works great and is a natural way to lubricate your nose.
During the dry winter months it's also a good idea to use a vaporizer or humidifier in your home or bedroom to keep the air moist which also prevents your nose from becoming dry and prevents nosebleeds too.