In Maseru, there are several internet cafes, although fairly cheap (usually LSL0.20-0.50 per min) they are pretty slow at best.
The cellphone network is OK in the towns, but fair out in the countryside. The only British cell phone network that has a roaming agreement is Vodafone. There are two mobile operators in Lesotho, Vodacom and Econet Telecom Lesoth. Vodacom has the widest coverage outside the towns, but is the (more) oversubscribed, and hence the less reliable. You can buy a Vodacom or Ezicel Buddie pay as you go sim card for under LSL50 in Maseru — worthwhile if you are staying for a while. Cellphones are available for hire in Maseru. Lesotho uses GSM900. The networks are pretty good now; both have 4G options.
If you have a South African Vodacom Sim Card, you can use it in Lesotho only on the Vodacom network. Be sure to enable roaming.