I just started fishing a lake that has walleye. They have a rule where you can not use minnows. any tips on how to catch walleye without using minnows.

Thanks for any tips and advice

Use night crawlers

see above - night crawlers work really well for 'eyes. In fact, a spinner/worm harness is one of my go-to baits for walleye.
Also, leeches work well during the summer.
Bucktail jigs, tipped with a piece of nightcrawler works on may lakes
"blade baits" like Heddon Sonar, or Reef Runner Cicada also work really well.
Stick baits (rapala minnows, shad-raps, husky-jerks, thundersticks, reef runners, etc) are effective artificials for walleye too. especially in the spring and fall when you can cast them from shore in the evening. They also work well on top of weed beds during the late spring and summer.

If you feel that you have better luck with minnows, and really don't want to stray too far from live ones, the newer Gulp! minnows are a nice artificial substitute. I use them in place of fatheads when I fish for perch.

I very seldom use live minnows at all for several reasons. First, they are a pain to keep alive. Second, with the new baitfish regulations in NY to prevent the spread of VHS, it's too much of a hassle. When I was a teen, I used to catch my own, nowadays, you pretty much are forced to buy "certified healthy" minnows from baitshops. I've found keeping baitshop minnows alive is even more of a pain than keeping ones you catch yourself.

There are lots of options for walleye that don't involve live minnows. The ones above are just a few. Experiment and find what works for you where you fish.