This verb first appeared in the Qenya Lexicon of the 1910s in its root form ᴱ√LEHE “come, be sent, approach”, with a past tense lenge (QL/52). At this point its Qenya stem form is probably something like ᴱQ. ✱lé-, since “h ... between vowels > ɣ > vanished” in the early Qenya of the 1910s (PE12/18). The English-Qenya Dictionary of the 1920s had a similar verb ᴱQ. lehe- or ᴱQ. lehta- “ride”. See the entries for √LEN and √LED for later iterations of these roots.
Early Quenya
lehesta
noun. ride, riding, raid
lehta-
verb. to ride, move (tr.)
lehtasta
noun. ride
lepta
noun. finger
let
noun. finger
faika
adjective. free
faire
adjective. free
lehe-
verb. to ride
tenge
noun. finger
tenna
noun. finger
A noun for “finger” in the Qenya Lexicon of the 1910s under the early root ᴱ√TENE “touch, feel” (QL/91). It was also mentioned in the contemporaneous Poetic and Mythological Words of Eldarissa, but with -nd- written above it indicating a variant form tenda (PME/91). A similar word tenge “finger” appeared Early Qenya Word-lists of the 1920s (PE16/137), but ᴱQ. lepta was written next to it, perhaps as a replacement, since after this point finger-words were primarily based on √LEP.
A noun appearing as ᴱQ. lehesta “riding, raid” in the Early Qenya Grammar of the 1920s (PE14/45, 75). In the contemporaneous English-Qenya Dictionary, it was lehesta or lehtasta “ride” based on the verb ᴱQ. lehe or lehta “ride” (PE16/132).
Neo-Quenya: For purposes of Neo-Quenya, I would update the noun to ᴺQ. nortasta “a ride” based on the later verb Q. norta- “to ride”. For “riding” as a general activity I would just use the gerund nortie.