Everything I'm seeing shows her as Johanna de Lacy:
This is from her son's profile:
Hawise de Lancaster
1,2,3,4,5
b. circa 1220
Father Sir Gilbert FitzRoger, Lord Kendal2,3,4,5 d. b 13 Jun 1220
Mother Helewyse de Lancaster3 b. c 1177, d. a Sep 1226
Hawise de Lancaster married Sir Peter II de Brus, Baron Skelton, son of Peter I de Brus, Baron Skelton & Danby and Johanna de Lacy ; They had 1 son (Peter III) & 5 daughters (Joan, wife of Peter de Mauley; Agnes, wife of Sir Walter de Fauconberge, 1st Lord Fauconberge; Lucy, wife of Sir Marmaduke de Thwenge; Margaret, wife of Robert de Roos; & Laderina, wife of Sir John de Bellew).2,3,4,5 Hawise de Lancaster was born circa 1220.
Family
Sir Peter II de Brus, Baron Skelton b. b 1201, d. bt 7 Sep 1240 - 7 Sep 1247
Children ◦Peter Brus, 6th & last Baron of Skelton Castle d. 1272
◦Joan de Brus+ d. b 13 Oct 1243
◦Laderina de Brus+3 d. a 1268
◦Agnes de Brus+3,4 d. 22 May 1286
◦Margaret de Brus+2,3,5 d. c 30 Jan 1307
◦Lucia de Brus+3 b. c 1239
Citations
1.[S767] Unknown author, The Complete Peerage, by Cokayne, Vol. V, p. 269.
2.[S16] Douglas Richardson, Magna Carta Ancestry, 2nd Edition, Vol. III, p. 295.
3.[S4] Douglas Richardson, Royal Ancestry, Vol. I, p. 215.
4.[S4] Douglas Richardson, Royal Ancestry, Vol. II, p. 548.
5.[S4] Douglas Richardson, Royal Ancestry, Vol. IV, p. 301.
http://our-royal-titled-noble-and-commoner-ancestors.com/p353.htm#i...
This link shows the same info:
https://our-royal-titled-noble-and-commoner-ancestors.com/p433.htm#...
Father John de Lacy, Constable of Chester1,3 b. c 1145, d. 11 Oct 1190
Mother Alice FitzRoger1,3 b. c 1150, d. b 1211
Johanna de Lacy married Peter I de Brus, Baron Skelton & Danby, son of Adam II de Brus, Baron Skelton and Ivetta d' Arches; They had 1 son (Peter II).1,2
Family
Peter I de Brus, Baron Skelton & Danby d. 12 Feb 1222
Child
Sir Peter II de Brus, Baron Skelton+1 b. b 1201, d. bt 7 Sep 1240 - 7 Sep 1247
Citations
[S4] Douglas Richardson, Royal Ancestry, Vol. I, p. 214-215.
[S4] Douglas Richardson, Royal Ancestry, Vol. III, p. 463.
[S4] Douglas Richardson, Royal Ancestry, Vol. III, p. 462.