Lemvig takes its name from Lem Vig, a bay on the western Limfjord and part of the broad water called Nissum Bredning. The original settlement occupied a flat strip between the fjord and Lemvig Lake, boxed in by steep slopes east and west that the last ice age left behind. There was nowhere to go but up, so the town gradually climbed the valley sides, which is why the streets still tilt. The harbour faces the fjord and is defended by a concrete seawall, because westerly storms shove North Sea water into the Limfjord and pile it against the town. Copenhagen is 375 kilometres away. The North Sea is ten. For centuries that ten kilometres might as well have been a hundred: the sandbars to the north sealed the fjord off, and Lemvig's ships had to work the inland shipping route toward Thy. A storm surge broke through the Agger Tange in 1825, and another opened the Thyborøn Kanal in 1862. Only then did the open sea arrive at Lemvig's door.

The town first appears in a pair of royal letters from 1234 and 1237, written as Læmwich and Lemvich. Through the Middle Ages it stayed very small — a church and not much else. A fire destroyed the town hall in 1479. In 1542 King Christian III ordered a school established here, and Lemvig held market town rights certainly by 1545 and possibly as early as 1471. A priest's report of 1638 sums the place up without flourish: "a small market town." That was still roughly true two centuries later. The nineteenth century changed it. Trade thickened, and by the turn of the twentieth century Lemvig supported a tobacco factory, a brickworks, a steam mill and a printing house, and read three newspapers at once — Lemvig Avis, Lemvig Dagblad and Lemvig Folkeblad.

The railway reached Lemvig in 1879, and the station still serves the Lemvig line running south into the national network. There is also a grass airstrip on the edge of town, EKLV, the kind of field where a Cub can land between showers. The modern economy leans on metal, wood and furniture, and the biggest employers include KK Electronics, the machinery maker Egholm, the Danish Coastal Directorate — whose job on this shoreline is never finished — and the pesticide works out on Harboøre Tange that the town still calls Cheminova. After the Second World War the town spread into the new suburbs of Østerbjerg and Rønbjerg Hage, and the population reached 6,371 by 1965. Sixty years later it stands a little under 6,800.

Lemvig Kirke stands at the centre of town. Its tower once ended in a high, sharp spire; a major rebuilding in the 1930s replaced it with the onion dome that now gives the skyline its unmistakable silhouette from the water. Johanneskirken, consecrated in 1883, belongs to the Grundtvigian tradition and was built by the architect Andreas Bentsen with the help of apprentices from Vallekilde Folk High School. Down along the fjord runs the Skulpturstien, a sculpture path carrying fifty-four works by Torvald Westergaard, who lived from 1901 to 1988 and left more of himself in this town than most artists leave anywhere.

For a town of under seven thousand, the export record is remarkable. Thøger Larsen, born in 1875 and dead in Lemvig in 1928, worked here as a surveyor's assistant and edited Lemvig Dagblad from 1904 to 1923. He was also a serious amateur astronomer who published a collection of astronomical studies, Stjerner og Tid, in 1914 — the same year he wrote "Danmark, nu blunder den lyse nat," now part of Denmark's cultural canon and sung at midsummer across the country. Jens Christian Skou was born here in 1918 and won the Nobel Prize in Chemistry in 1997 for his work on the sodium-potassium pump; he died in 2018, aged ninety-nine. The jazz singer Sinne Eeg was born in Lemvig in 1977. So was the eighteenth-century Norwegian chronicler and meteorologist Jacob Nicolai Wilse, in 1736, and the handball player Jannick Green, who took Olympic gold with Denmark in 2016.