Though I can't answer the question of whether "George Lucas ever stated explicitly that he based something on another thing he saw in Star Trek," I can answer your previous question statistically:
The null hypothesis that "the instances of cross-reference between Star Wars and Star Trek are coincidence or delusion" is rejected at significance level a = 0.01. One must conclude that the references were deliberate.
Why? I believe it is because the same people worked on both series of films. The missing link here is a little company George Lucas founded in 1975 called Industrial Light and Magic.
Go a head and search for the term "Star Trek" on IL&M's Wikipedia page.
You will realize that the Lucas-owned firm produced the visual effects for many of the Star Trek films, as well as Lucas' own. In fact, IL&M represented the cutting edge in visual effects at the time and has, to this day, gone on to produce the visual effects for many high-grossing films. Though they are now owned by Disney by virtue of Disney's acquisition of LucasFilms, IL&M produced the visual effects for the most recent ST movies, as well.
What may be interesting would be to see if references to ST/SW appear in other IL&M produced films.
Apologies if y'all already knew this, have assumed the connection, and I'm just waxing poetic. I just learned this a few weeks ago and mind = blown.