For the sake of anyone looking at these same questions in the future I'll at least add my notes, although I have not worked this out.
1350. For anyone interested it seems that the first John Lestraunge of Walton d'Eiville, husband of Ida, may have died before 1350, when Ida appeared representing family interests. See
http://discovery.nationalarchives.gov.uk/details/r/C9440253
1367. A reference to John Le Straunge "of Walton" going overseas, or at least being allowed to assign attorneys, can be found in the Patent rolls for that year. No mention of a wife yet, neither a Mabel nor an Elizabeth, at least in the calendar.
https://hdl.handle.net/2027/mdp.39015031081105?urlappend=%3Bseq=17
1376. The references in HOP and BHOL are both to the calendars of the Close Rolls. These were both done in Itchington, the manor of the Oddingseles, which makes the HOP explanation very believable, but surely the writer must have looked at some other records not being cited? The calendars do not mention any contracts being attached concerning marriages. The grants are superficially from one branch of Lestranges to another, and the two branches had done some swaps in the past.
"Writing of John Lestraunge lord of Walton, being a letter of attorney appointing John Huwet and Richard Warner of Walton to deliver to Roger Lestraunge, Philip vicar of Wellesborne and William de Offechirche clerk seisin of all the lands, rents, services and reversions which he the said John Lestraunge had in Alcrynton, Balscote and Wroxton co. Oxford, Shenyndon co. Gloucester, Tysho, Pylardynton and Lockesleye co. Warrewyk, Totebache, Bradele, Evesham and Goldecote co. Worcester, according to his charter to them made. Dated Long Ichynton co. Warrewyk, Thursday after St. Bartholomew 50 Edward III.
Memorandum of acknowledgment, 8 November."
"Charter of John Lestraunge lord of Walton, giving to Roger Lestraunge, Philip vicar of Wellesburne and William de Ofchurch clerk, their heirs and assigns, all the lands, rents, services and reversions which he had in Alcrinton, Balscote and Wroxston co. Oxford, Shemyndon co. Gloucester, Tysho, Pilardynton and Lokesleye co. Warrewyk, Totebache, Bradele, Evesham and Goldecote co. Worcester. Witnesses: Sir John Oddyngseles knight, Sir John Verdoun knight, Richard Boteler, William Palmer, John Baylli of Southam. Dated Long Ichinton co. Warrewyk, Thursday after St. Bartholomew 50 Edward III.
Memorandum of acknowledgment, 18 October."
Another record comes from the Feet of Fines.
http://www.medievalgenealogy.org.uk/fines/abstracts/CP_25_1_288_50.shtml
CP 25/1/288/50, number 796.
Date: One week from St Martin, 50 Edward III [18 November 1376].
Parties: Roger Lestrange, Philip, the vicar of the church of Wellesburne, and William Offechurch', clerk, querents, and John Lestrange of Walton' and Mabel, his wife, deforciants.
Property: 8 messuages, 4 tofts, 12 virgates of land, 6 acres of meadow and 6 shillings and 8 pence of rent in Alcrynton', Balscote and Wroxton' in the county of Oxford and 1 messuage, 4 virgates of land and 4 acres of meadow in Shenyndon' in the county of Gloucester and 2 messuages, 5 tofts, 9 virgates of land and 14 acres of meadow in Euesham, Totebache, Bradle and Goldcote in the county of Worcester.
Action: Plea of covenant.
Agreement: John and Mabel have acknowledged the tenements to be the right of Philip, and have remised and quitclaimed them from themselves and the heirs of John to Roger, Philip and William and the heirs of Philip for ever.
For this: Roger, Philip and William have given them 200 marks of silver.
As mentioned already, even if a marriage was being arranged it does not seem to make sense that it would be the marriage of John Lestrange of Walton, who was married already and whose widow survived him.
1397. What happened in 1397? I can find nothing explaining the HOP comment "However, the Maurewards’ tenure of these Strange estates was to be disputed in 1397, and it is unclear whether they were able to retain them for the rest of Elizabeth’s life." The footnotes are in awkward blocks, and to secondary sources. The only one I can't check is Farnham's Leicestershire Village Notes II.75. Does anyone have access to that?
The Lestranges of D'Eiville were a junior branch of the main Knockin line, who eventually "daughtered out" but the two heiresses married into the better known junior line, the one in Hunstanton, Norfolk. For this reason they will have many modern descendants, although they are not well-known. The line goes:
1. John
https://www.wikitree.com/wiki/Strange-850
2. John (son)
https://www.wikitree.com/wiki/Strange-852
3. Alan (son) who died overseas with Henry V.
https://www.wikitree.com/wiki/Strange-853
4. Thomas (brother)
https://www.wikitree.com/wiki/Strange-854
This Thomas's son Thomas died at Bosworth, it seems, and it was his daughters who married into the Hunstanton family.