Having spent 35+ years studying the Lynns of Ulster and Scotland, I've found Lynns who were weavers living in four different counties of Ulster - Antrim, Derry, Fermanagh, and Tyrone. So, no, occupation is no help connecting Lynn families. It may be important to note, however, that weavers often - perhaps usually - grew their own flax.
Also, the tradition that any particular Lynn family were Huguenots may or may not be accurate. The only historical account I've found on the subject is a chapter in "History of the Presbyterian Church in Ireland" by James Seaton Reid, D.D., in which Reid stated that Rev. Charles Lynd and his parents were "a French Protestant family in Normandy, one of the numerous refugee-households whom the tyranny of Louis XIV, compelled to fly from France in the end of the seventeenth century." Reid goes on to say that the Lynd family settled in Ramullan, County Donegal and that Rev. Lynd went from there to Coleraine. The spellings Lynd and Lynn were sometimes interchanged. The ancestor of a distant cousin of mine wrote his name as Lynd in an 1810 journal while his sons almost always went by Lynn.
In any case, even Reid's account may be in doubt. Nicholas Pynnar in his 1619 survey of the Ulster plantation wrote that Scots settler William Lynne was then in possession of Carrowreagh, County Donegal. Nephews William Lyne and David Lyne were in possession thereof as late as 1654. Rev. Charles Lynd gained possession of Carrowreagh at some point and sold it in 1744. Unfortunately, there seems to be no record of ownership of the property in the intervening 90 years.
One thing is certainly true. A great many Lynns in Ireland were Ulster Scots while some were Irish, the latter having derived their name from Flynn/O'Flynn.