Joan Assenhull (de Burgh)

• HASILDEN, Thomas I (c.1322-c.1387), of Wakefield, Yorks. and Steeple Morden and Guilden Morden, Cambs.
• b.c.1322, ?s. of Christopher Hasilden.1 m. (1) 2s. Richard* and Thomas II*; (2) Joan (d. bef. 1433), da. of Sir John Burgh (1328-93) of Burrough Green, Cambs. and Swinton, Yorks. by his 2nd w. Katherine, da. of Sir John Dengaine† of Teversham, Cambs.; half-sis. and coh. of Thomas Burgh (d.1411).
• From: http://www.historyofparliamentonline.org/volume/1386-1421/member/ha...
• __________________
• ASENHILL, alias HARPEDEN, William (d.1443), of Guilden Morden, Cambs. and Walton, Yorks.
• m. bef. Nov. 1404, Joan (d. bef. 1433), da. of Sir John Burgh (1328-93) of Burrough Green, Cambs. by his 2nd w. Katherine, da. of Sir John Dengaine† of Teversham, Cambs.; half-sis. and coh. of Thomas Burgh (d.1411), and wid. of Thomas Hasilden I* (d.c.1387) of Guilden Morden, 1da. Kntd. bef. May 1416.
• From: http://www.historyofparliamentonline.org/volume/1386-1421/member/as...
• ___________________________ https://books.google.com/books?id=ZbkHAAAAQAAJ&pg=PA21&lpg=PA21&dq=...

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Not seeing where Lucy was this Joanna's mother. The sites linked on Joanna's father Thomas' profile show her father was married to Margaret Waldegrave, as do other sources. It's laid out very clearly on the stirnet link below although that site just lists her mother's maiden name as Waldegrave but doesn't give her first name.

This Thomas is not connected to the de Burg/de Burgh family of Cambridgeshire (which is charted on Stirnet's "BZmisc16" page (membership required to view without interruption)).