Lost Dog Wash has several unpaved, dirt trails for you to hike, and dogs are allowed. However, there are a lot of loose rocks on the trail and cholla and other cacti spikes are everywhere, so be very cautious about where you step. One person in our party got cholla'd and my dog stepped on a cactus spike, so be sure to bring tweezers and a comb to pick out spikes, and to comb any cholla pads off you. On a warm day, the trail can be rough for dogs not so used to hiking so bring lots of water and take frequent breaks as needed.
The actual hike itself isn't too bad, and you get a great view of the city once you reach higher elevations.