A while back I posted a question asking for details about crossing from the Lower Omo into Kenya's Turkana region and promised I'd post the results. I'm not sure if anyone cares, but here it is anyway.
Crossing from Omorate, the southern-most city, is NOT possible. In fact within minutes of arriving I was tracked down by a local policeman and told that I wasn't even allowed to be in the city without a guided tour group. And I definitely wasn't allowed to cross. He stayed with me until the next truck came to take me out of the city.
That being said, I think that it would be possible to try to crossing from the SOUTH, if anyone is ever willing to give it a go. I've heard of a couple people over the years who have succeeded, though from what I can tell it's best to get a local guide because it's easy to get lost on the 50+ kilometers of walking from Lake Turkana to Omorate. And you don't want to get lost here, especially with all the armed locals.
You would have to drive up to Loki from Lodwar to get a Kenyan exit stamp, back to Lodwar, and then up the lake as far as you can go before the road peters out. You might be able to get a lift with aid workers or other trucks for some of that walking, but be prepared to go long distances on foot. And Turkana's water is not drinkable, though you should be able to get some at most stops along the water, not to mention when you cross the Omo River in Ethiopia.
