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.