Surtees's Conyers pedigree says Eleanor Conyers married 1st Lancelot Strother of Newton and had issue. Looks good for them. Question is whether any emigrated.
That Lancelot (son of William) wasn't the only Lancelot. There was a Lancelot Strother son of Henry, of Hallywell in Alnwick.
Eleanor and Lancelot may well have had a son William, as there's a William Strother of Kirknewton, esq, in 1657.
We have Strother-136 born at Alnwick. If that were definitely correct, it would suggest he's attached to the wrong family. But it could be just the usual random box-filling.