Well I had a very messy old webpage about them which I can mail you. There were several marriages between Lancasters and Lowthers over the centuries.
Unfortunately my internet provider decided to stop supporting websites in recent months. Today the wayback machine is down but the URL used to be
users.skynet.be/lancaster/Lancasters%20of%20Sockbridge.html . I will try to get the best pages up again somewhere. All proposals welcome. Maybe just a google site?
There was a relatively extensive discussion in an article by Rev. Ragg in TCWAAS in 1910, but that does not supply the whole story, and it contains at least some mistakes. My webpage attempted (not always successfully) to patch together a bigger story, or at least delineate some of the main options. I was assisted greatly by David Hall. Of course the period you are talking about is right at the end of the line. Here is some of what I had on that page...
The son of Richard Lancaster of Sockbridge and Barbara Lancaster from Crake Trees:
Christopher Lancaster of Sockbridge Esquire, was heir to both the main Sockbridge line, and the Crake Trees line. He died about 1641 and married Elizabeth Tankard, daughter of Thomas Tankard, who was a relative of Christopher's recusant aunt? (Nicolson and Burn).
In the Lowther archives the following record exists: Grant of wardship of Christopher Lancaster heir to part of the manor of Waitby and property in Oddendale and Crosby Ravensworth D LONS/L5/1/15/5 1614.
His uncle Lancelot Lancaster of Sockbridge (approx 1568-1642) was still alive when he wrote his will. He wanted lands in Waitby and Penrith, apparently not connected to his uncle, to be sold for the advantage of his younger daughters before his uncle died. The lands in Sockbridge, Hartsop and two other places could, if I understand correctly, be taken over by the Lowthers after his uncle's death, if they paid off the other sisters for a very large amount of fifteen hundred pounds?
Strickland Roger appears to have been sold in 1623, to "Hugh Barrow of Skelsmergh, yeoman and Mathew Phillipson of Strickland Roger, yeoman", so it did not end up with the Lowthers.
https://archiveweb.cumbria.gov.uk/CalmView/Record.aspx?src=CalmView.Catalog&id=WDX+1526/4/3&pos=77
The will mentions an uncle Lancelott, and his wife Francis, as well as John Lowther, Christopher Lowther, and Leonard Dykes. The names of his four daughters agree with the account of Nicholas and Burn, of which Francis was to marry Christopher Lowther, and his wife was Elizabeth.
A house was also conveyed by a Christopher Lancaster to a John Robertson, in Sockbridge in 1647 D LONS/L5/1/34/4. Possibly a relative of his mother?
My old webpage also says that Lancelot and Richard of Sockbridge were sons of Edward Lancaster of Sockbridge (approx 1538-1618) and Margaret Middleton, daughter of John.
Edward's father was the more well-known Lancelot Lancaster esquire, of Sockbridge (approx 1490-1570). Lancelot was steward of Lord Dacre. In 1547-1549 he was escheator for Westmorland. The historian of Mervyn Evans James wrote that "he could be relied on, when required, to push his masters quarrels with the dominant local Clifford interest to the point of violence".
Lancelot was son to William Lancaster of Barton or Sockbridge (approx. 1465-1510) and Elizabeth Lowther. William Lancaster is the effective continuation of the main line, because he married Elizabeth Lowther, great grand daughter of William Lancaster of Sockbridge, brother of his own great grand father Hugh Lancaster, and thereby apparently re-took control of Sockbrige, if it had ever effectively been lost.