It wasn't a lack of time that made this episode suffer. It was a lack of a story. There was too much padding.
Bingo. Even the best scene, where Kirk and Spock figure out what the frick was going on, feels bloated. With many episodes, you feel like there are scenes they could have filmed and didn't; with this one, they just repeated or expanded to pad the slender thread of a story. Plus, we have yet another interloper wandering unsupervised through the Enterprise. ("Where is he?" "I don't know, Jim. This is a big ship. I'm just a country doctor.")
Now if, say, Lietenant Masters was in love with one of the Lazari, but creeped out by the other, there would have been some human interest there. Something would be happening up there on the screen to keep my mind from wandering or nodding off.
I agree; it seems to me that this was the basic idea, that she was the focus through which the audience got the puzzle pieces of the story, and when the scripted interaction between she and the Lazari was nixed by NBC, there was nothing left to help the audience figure out the plot, such a it was.
What makes the episode so frustrating, I think, is that at the core there is the potential for an interesting story.

Just adding in a romance, without having enough time to properly explain the stuff about the two Lazari, would not have saved it.

That they didn't do a good job with a single episode which included meaningless stuff, doesn't prove that just eliminating the meaningless stuff would have been enough.
No. I'm saying they should have eliminated all of the redundant stuff and replaced it with a story about human interaction. This would have added some meaning and, if done well, some pathos.
a two-parter might have been in order.
NOOOOO!!!

That they didn't do a good job with a single episode which included meaningless stuff, doesn't prove that just eliminating the meaningless stuff would have been enough.
So that's how you see it, but I think they definitely needed more time to tell that kind of a story. In a way it's like they were having two episodes - one with each Lazarus - instead of just one, so a two-parter might have been in order.
One example: In the TNG episode "Cause And Effect" they were able to show a few passes through a time loop - far fewer than "really happened," it turns out - in an effective way to relate the story. But that was still about just a single event. If there had been two events - or two Lazari, in this case - involved, I just don't believe a single episode was enough time.

It wasn't a lack of time that made this episode suffer. It was a lack of a story. There was too much padding. Lazarus falls off a cliff. Lazarus gets treated in sick bay. Lazarus beams down. Lazarus falls off a cliff. Lazarus gets treated in sick bay. Lazarus tells some more lies. Kirk and Spock banter some ideas and unconvincingly stumble into the truth. Interspersed among all of this, Lazarus fights himself in scenes that take too long and are barely coherent. Almost all of it could have been cut or trimmed without losing the "story".
Now if, say, Lietenant Masters was in love with one of the Lazari, but creeped out by the other, there would have been some human interest there. Something would be happening up there on the screen to keep my mind from wandering or nodding off.

The Alternative Factor didn't really have enough time for a coherent story as it was. Adding any romance sub-plot would have been a terrible idea.

For the record, the first interracial kiss on
Star Trek
happened in Season One, "What are little girls made of," when Uhura kisses Christine Chapel.
What may have been courageous about "Plato's Stepchildren" is if Fred Freiburger had managed to plan an interracial kiss in a romantic setting, rather than one that occurs under duress (and compulsion) between two people who have no emotional involvement. Controversial, but something less than groundbreaking, more of a footnote.
There was supposed to be a sub-plot in Season One "The Alternative Factor" of a romance between a white guest-star (one of the Lazari) and an African American engineer, but presumably the Network put the kibosh on it, forcing rewrites, and is one of several reasons the episode dwells in
Star Trek
infamy as the nadir of Season One.

Gialmere; thx, had no idea they were that far apart.

Gialmere; are you sure? The Wild Wild West predates TOS by only 1 yr.
According to IMDb, the first season WWW episode,
The Night the Dragon Screamed
, first aired on January 14, 1966. The third season ST episode,
Plato's Stepchildren
, first aired on November 22, 1968. So, officially, it's a difference of 2 years, 10 months, 1 week and 1 day.

Gialmere; are you sure? The Wild Wild West predates TOS by only 1 yr.

There might have been an Asian-American kiss on TV before Star Trek. I read this recently, but remember the program.
On a first season episode of
The Wild Wild West
, James West shares several kisses with a Chinese princess (played by a Filipina actress) and seems very happy to do so. This would have been around three years before Plato's Stepchildren.

Julia
was fairly revolutionary. It was only the second American series to star a black woman.
https://en.wikipedia.org/wiki/Julia_(TV_series)
It was difficult to locate this article, it having somehow fallen through the Wikipedia indexing cracks. I found it only by entering "Julia Baker", then rejecting Wikipedia's attempt to replace the search with "
Julian
Baker".

Sono white guy kissed "Julia"?

No, they did not kiss. Petula merely
touched
his arm. Here's a little article what talks about the whole thing, from
http://www.emmytvlegends.org/blog/?p=1086

What was the uproar with Harry Belafonte and Petula Clark? Did they kiss?

There might have been an Asian-American kiss on TV before
Star Trek
. I read this recently, but remember the program.

You guys know their lips never actually touched, right.

How? Desi Arnaz was Caucasian.
So you're saying Hispanics like Desi are white and not "people of color"?

Vhris 109; There are Spanish Hispanics, Negro Hispanics, Asian Hispanics. Even Native American Hispanics! But no White Hispanics. Not in America (U.S.A.), anyway.

He was a 'white hispanic'.

Didn't Lucy and Desi share an interracial kiss?
How? Desi Arnaz was Caucasian.
IMDB, flagging ppl for bull
since 1995.

Was it Lionel Jefferson & Archie's niece.

Thanks doug65 for the correction. I guess I'd forgotten that we were talking just television. Late night, you know how it is?

You're correct about "One Potato, Two Potato." However, that was a
feature film
rather than a television program - that's where the distinction lies.
The first interracial kiss on American network television was in the episode "Plato's Stepchildren," which aired on November 22, 1968 when Captain Kirk kissed Lieutenant Uhura.