A suggested origin of the name Lathom is hlatha, Old Norse word for barn. That may explain why there are several places with variants of the name in Lancashire and Yorkshire.
Lathom House in Lathom near Ormskirk, Lancashire was built by a member of the Stanley family (Earls of Derby) after a Stanley married a Latham heiress, daughter of Sir Thomas Latham. It was a key stronghold in northern England in the civil war. Stanley was executed 1644.
Other notable Latham/Lathom families in Lancashire, mainly Royalists and recusants:
Lathom of Mossborough near Rainford. Mossborough House was in the possession of the de Lathom family from 13th-17th centuries, then a Molyneux through marriage and later sold to Earl of Derby. Henry Lathom of Mossborough was on a list of recusants who compounded their fines in 1629 ("Lancashire Catholic Recusants about 1630" article by J. Brownhill published by Historical Society of Lancashire & Cheshire*)
Lathom of Allerton near Liverpool.
Lathom of Parbold
I have a tenuous connection to William Lathom of Tarbock, near Prescot. His grandson, also William was a relative of a 4x great-grandmother. A daughter of the elder William may have been my 6xGGM and grandma of the aforesaid 4xGGM. William Lathom the grandson was a militia officer in Ireland for part of the war against Napoleon.
*Quotation from article "Catholic Recusants about 1630" "King Charles ... (who had been drawn into a war by his Parliament ...) offered to maintain 5000 men to serve his majesty in Ireland ...".