Lesotho is a hiker's paradise and you can hike just about everywhere. Day hikes are available at all the accommodation establishments.
Its recommended one always takes a local guide - makes the trip more interesting and they can help with communication when you meet passes by. Official Overnight Hiking with local guides and in some cases, slackpacking, with a packhorse to carry your luggage is available at the established lodges like Malealea, Semonkong, Ramabanta. The others mainly cater for day hikes, but if the push comes to the shove will be able to organize an overnight hike at a moments notice.
These are our picks but there is a whole country full of mountains and overnight hiking can be organized just about everywhere if you chat to the locals and organize a guide.