In the country of lesotho a king is the head of state but a prime minister holds governmental power. this is an example of what form of government?

This is an example of "parliamentary" form of government.

A parliamentary system of government implies that the official part of government has the immediate or aberrant help of the parliament. This help is generally appeared by a vote of certainty. The connection between the official and the council in a parliamentary framework is called capable government.  

Parliamentary systems for the most part have a head of government and a head of state. They change after their terms are finished. The head of government is the executive, who has the genuine power. The head of state might be a chosen president or, on account of an established government, inherited.

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