This root and ones like it were used as that basis for “wide” adjectives throughout Tolkien’s life. The earliest iteration of this root was unglossed ᴱ√LAŘA [LAÐA] in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. landa “wide, broad” and ᴱQ. lar “region, place” (QL/51). In the contemporaneous Gnomish Lexicon there was G. land “broad” (GL/52). In The Etymologies of the 1930s the root became ᴹ√LAD with derivatives like ᴹQ. landa/N. lhann “wide” (Ety/LAD); in this document it was related to both ᴹ√DAL “flat” and ᴹ√LAT “lie open”.
The root was mentioned in the Quenya Verbal System of the 1940s with the gloss “lie flat, be flat”, distinct from the root ᴹ√LAT glossed “be extended, stretch, be situated (of an area)” (PE22/126). √LAD was mentioned again as Quenya-only variant of √DAL “bottom, ground” in a list of roots from the late 1950s or early 1960s (PE17/150). However, it clearly survived in Sindarin as an element in the names Landroval “Broad Winged” (LotR/948; PE17/63) and Lothlann “Wide and Empty” (S/123), not to mention úlan(n) “not broad, narrow” (PE17/144).
One tricky thing about this root was that Tolkien seems to have abandoned √DAL on which it was originally based, given the change of S. dalath “plain” to S. talath “plain”. However, I think it is likely that √LAD survived, perhaps as a variant of √LAT.
Neo-Eldarin: For purposes of Neo-Eldarin, I would assume √LAT refers to openness, where √LAD refers to flat or wide things.
This root first appeared in The Etymologies of the 1930s as ᴹ√DAL with the gloss “flat” and various derivatives of similar meaning (Ety/DAL). It reappeared again in later notes as √DAL “bottom, ground” written in the late 1950s or early 1960s (PE17/150). In both places, it had a variant form √LAD of similar meaning.
One notable derivative from the 1930s was N. dalath “plain” which appeared in the name N. Dalath Dirnen “Guarded Plain” in Silmarillion drafts from the 1930s (LR/299). But in the second note mentioned above, Tolkien said “X Dalath Dirnen. dalath won't do = plain ... TALAT = ground (bottom), hence TALAT = fall down” (PE17/150). Indeed, in later Silmarillion drafts, Tolkien changes this name to S. Talath Dirnen (WJ/140). This may mean that Tolkien ultimately rejected this root, but the variant √LAD probably survived: see that entry for details.