Hey Duan,
Welcome to the site. To go on the west side of Lake Turkhana, you have to cross the river at the top of the lake which involves negotiating with small boats to carry you across so not ideal or guaranteed.
The east side is pretty rough with not very many settlements so will meet your adventure needs. You'll have to carry fuel and water but a small number of bikers ride it every year so it's certainly doable. Some hook up with a 4X4 to ligten their load and make the riding more enjoyable. Have fun.
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