The oldest part of the church is the Romanesque nave, built in round-arch style during the first half of the thirteenth century, reportedly by Cistercian monks. Tradition links the church to the cult of Saint Olof, suggesting it may have served pilgrims passing through the area. In the 1280s, income from trade with other countries allowed the church to be enlarged, though the upper part of the west gable was never completed in medieval times and was only finished off, in masonry, during works in the mid-twentieth century.
The interior was replastered in 1805 and redecorated in 1807, when dark ornamental borders were painted around the vaults, pillars and window recesses, and a new wooden floor was laid. The most far-reaching intervention came in 1958–1960, under architect Åke Porne, when a leaking roof—a recurring problem for centuries—was finally addressed with a new copper roof and a smaller copper-clad ridge turret, said to be unique among Gotland's churches. The uneven medieval walls were also rendered with concrete during this campaign.
Among the church's furnishings, the grey limestone font, carved around 1200 by the stonemason Sighraf, and a large altar cabinet made in Lübeck in the early fifteenth century are of particular note. The church's only surviving medieval wall paintings are found on the blocked-up tower arch, and its triumphal crucifix is said to be the largest in the Nordic countries, though such claims of superlative status are difficult to verify independently.
Lau kyrka is perhaps best known for its exceptionally long reverberation, reported at around twelve seconds, which has drawn composers and recording artists to write and perform music specifically suited to the space; some recordings are said to have been made only because of this acoustic quality. The reverberation reportedly shortened slightly after the old chairs were replaced with fixed pews. The church has had at least two organs: one moved here from Visby Cathedral in 1892, later replaced by a mechanical organ in 1960, and a further new organ installed in 2011.
Beside the church stands Kastalbacken, the ruin of a stone tower thought to have been a defensive kastal, built in the twelfth century for the protection of the local community. Only the lowest storey's two chambers survive, one retaining part of its vaulting, and the ruin is registered as measuring roughly 27 by 12 metres, with limestone walls up to two metres high—a reminder of the site's earlier strategic importance.