Yes you can safely leave a Himalayan Salt lamp on all the time.
In fact the Himalayan Salt Lamp will work best when left on all the time and it will have a much better affect at purifying the air and Ionizing it too when left on since it will always be warmed up.
A Himalayan Salt Lamp uses very little electricity and uses a low wattage bulb so they're not costly to run
Himalayan Salt Lamps are very safe to leave on all the time and that's what they're designed to do.
If you can leave a light bulb on in your home all the time then you can safely leave your Himalayan Salt Lamp on all the time too.
The Himalayan Salt Lamp provides maximum Ionizing benefits when fully warmed up.