On the English Wikipedia page for Muchland:

http://en.wikipedia.org/wiki/Muchland

Michael de Furness (1197-1219) is listed as married to Agatha Fitz Henry. He didn't carry the name "Le Fleming" like his grandfather and great grandfather.

Father: William de Furness (c1150-1203) Mother: Ada de Furnys Son: William de Furness

His title was Lord of Aldingham.

About his holdings:

Muchland derives its name from Micheal's Land after Michael le Fleming (great grandfather) who was granted the lands by Henry I sometime between 1107 and 1111. These lands lay eastwards of Abbey Beck and southwards of the moors of Birkrigg and Swarthmoor and stretched right down to the southern-most tip of the peninsula at Rampside.[1] At that time the southern limit of the manor was Walney Channel, but it was later moved inland to follow the line of Sarah Beck or Roosebeck. This land became the new manor of Aldingham

Reference:

1.^ F Barnes, Barrow and District, 1968