Your dates look about a century too early. If you got your tree off the internet, it might have been gerrymandered.
The Parbold line is discussed here
http://www.british-history.ac.uk/vch/lancs/vol6/pp178-181#anchorn9
and here
http://www.stirnet.com/genie/data/british/ll/lathom02.php
but the details are vague. However, there seems no doubt that they descend from Edward the younger son of Eleanor Ferrers
http://www.wikitree.com/wiki/Ferrers-141
she being the gateway to William the Conqueror and all points north.
Firm up your connection to the Lathoms and you're done. The rest is all in the standard places.