On the Lemosho route, you go to the toilet in the toilet tent provided by your tour operator when at camp. During the day's trek, you go to the toilet behind a rock or bush. But note that you can't leave any loo paper behind, as Kilimanjaro National Park has a 'leave no trace' policy. So you'll need to carry little disposable bags with you for carrying your used toilet paper till you reach camp.
It's worth noting that you need to pee all the time on Kilimanjaro, as discussed in 6 things I wish I knew before climbing Kilimanjaro. Also, climbing at altitude can bring on your period early. Ladies, you might find it useful to read Advice for women climbing Mt Kilimanjaro.