Lapworth was born at Faringdon in Oxfordshire. In 1864 he became a schoolmaster in Scotland where his interest in geology developed. There he studied the Lower Paleozoic rocks, publishing his results between 1878 and 1882. He used graptolites, the fossil skeletons of colonial animals found in the Lower Paleozoic, to determine the stratigraphy of Scotland and later published a series of monographs on the fossils (1901–18).

In 1879 Lapworth introduced the Ordovician system of geological strata. There had been a bitter dispute between Adam Sedgwick, who considered this complex series of strata to be Upper Cambrian and Robert Murchison, who considered it to be Lower Silurian. Lapworth's suggestion that it was in fact a separate system, which he named Ordovician after a Welsh tribe, settled the dispute.

Lapworth was appointed to the chair of geology at Birmingham University in 1881. His son, Arthur, was a chemist of some distinction.