Go up with your own car is forbidden. To get to the summit, you will have to buy ticket to take a seat in one of the pickups that go up and down between the parking at the bottom of the mountain and the cafe (with a terrace with nice view and very reasonable prices despite the lack of competition and the exceptional setting) 3.5 kilometers higher. Hang on, it shakes a little;) Thenre you will have to take a long way of stairs to reach the temple at the top. Better to have good shoes and be in shape. Take water before starting the climbing walk because up there no one sells drinks. And if you go with young children (I do not recommend it), watch them constantly. Half an hour's walk. Once you finish wisiting, you can go back done with one of the pickups that will bring you back to the car park.
Wat Chaloem Phrakiat Phrachomklao Rachanuson is located near Chae Hom over 60 km drive from Lampang city. There are local buses going there but the journey will be very long (at least 1h30 to arrive in Chae Hom) and once in Chae Hom, you will have to reach the temple car park from which the pickups take visitors to the summit (about 6 km away). I did not test it because I went by car, but according to Chiang Mai TAT Office, once in Chae Hom, if you walk 1 km towards the Green Gate you will find a car service 200m further which can take you there. But I would advise you to have your own vehicle or hire car with driver to come here. Knowing that in Lampang, it is quite easy to negotiate with one of the yellow and green cars (local buses) to privatize one to take you wherever you want. Otherwise, ask your hotel, if they can find you a car with driver. And do not hesitate to add other stops like a stop at Chae Son National Park and its hot springs..
Wat Chalerm Phrakiat is a temple and when you visit a temple in Thailand there are some rules to know and follow :