William Lindsay (III), son of David (I) (d.a.1241)
mentioned in pro anima clause highly suggestive that he had died, in charter of brother David (II) (3/350/14)
died before his brother David (II), thus before 1241 (perhaps well before)
William appears to have become involved in the Stewart family lands and interests in the west of Scotland:
probably the William Lindsay who appears alongside Walter Lindsay in major charter of Walter son of Alan (II) the steward to Paisley Abbey, 1208×1214 (Paisley Syllabus, no. 18);
probably the William Lindsay who witnesses Roger prior of Paisley’s charter, 1208×14 (Paisley Syllabus, no. 21);
probably the William Lindsay who witnesses a charter of Malcolm Lockhart anent land in Kyle Stewart, 1204×41 (3/355/2);
probably the William Lindsay, rather than William (II), who witnessed a charter of Peter son of Fulbert of Pollok to Paisley, probably soon before 1196. William’s position as last on the list suggests that he was young at the time. William (II) was a major baron and would have been given pride of place in this charter (Paisley Syllabus, no. 91; 3/473/2);
probably the William Lindsay who witnessed a 1230 charter of Alexander II to Paisley Abbey (1/7/164), alongside a David Lindsay (II).
Scots Peerage would assign these to a William, brother of David (I) and Walter (III), but there is no clear evidence for such a person ever having existed, and these seem to fit well with William (III), for whom we do have independent evidence. SP says that this William was a steward to the Stewart family, but offers no citations or references, and I presume this is based on a later oral tradition.
I would suggest that William was younger than David (II) but not necessarily younger than any of the other children, and that he had reached majority by 1196 and died sometime in the 1230s.