I'm not sure it can be proven beyond a shadow of a doubt, but it is at the very least, using Mythbusters' terminology "PLAUSIBLE".
An article "Lolita: A Probable Source of Nabokov's Name for his Temptress" (James T. Bratcher, Notes & Queries, September 2009) posits that:
For his novel by that name, Vladimir Nabokov probably took ‘Lolita’ from Mayne Reid's romance novel The War Trail; or, the Hunt of the Wild Horse (London, 1857).
While I don't have access to the full article (behind a paywall), this rings true:
Nabokov notoriously was heavily influenced by Mayne Reid, as noted by him in "Speak, memory" autobiography - chapter 10 can be read on Google Books.
The Wild West fiction of Captain Mayne Reid, translated and simplified, was tremendously popular with Russian children at the beginning of this century, long after his American fame had faded. Knowing English, I could savor his Headless Horseman in the unabridged original. Two friends swap clothes, hats, mounts, and the wrong many gets murdered—this is the main whorl of the intricate plot.In the summer of 1909 or 1910, [a friend] enthusiastically initiated me into the dramatic possibilities of the Mayne Reid books. He had read them in Russian.and, when looking for a playable plot, was prone to combine them with Fenimore Cooper and his own fiery inventions. I viewed our games with greater detachment and tried to keep to the script."
A very full discussion of the topic can be found in Don Barton Johnson's "Vladimir Nabokov and Captain Mayne Reid" published in "Cycnos Magazine, Volume 10 n1: NABOKOV : Autobiography, Biography and Fiction"
The referenced story, indeed, contains Lolita as a horse name as can be confirmed on Google Books or archive.org:
Sadness, not sup
plication, was the prevailing tone, which was further confirmed
as she knelt to the ground, pressed her lips to the muzzle of the
still breathing mustang, and exclaimed :
" Ay-de mi ! poire yegua ! muerte ! muerte /" (Alas me ! poor
mare ! dead ! dead!)
" A woman ?" said I, feigning astonishment. My interroga
tory was unheeded ; she did not even look up.
" Ay-de-mi ! poire yegua! Lola, Lolita !' she repeated, as
coolly as if the dead mustang was the only object of her
thoughts, and I, the armed assassin, fifty miles from the spot !
" Pohre Lolita '' she continued, " I have good cause to
grieve ; I had reason to love you well. More than once you
saved me from the fierce Lipan and the brutal Comanche.