Were they infected humans or aliens that looked human?

They were purple tubes that were given human bodies for their mission by the Big Giant Head, who could revoke the human bodies at any time. When they left earth, their bodies disappeared and they supposedly went back to being purple tubes.

I think that the aliens were given bodies of people that existed since Dick did look like that guy Mary knew from the 60s.i do remember them saying that they picked to be white and sally being commended on the form she took on.

I know their bodies disappeared when they left. However; Harry said when they leave, their human bodies will "expire."
Having said that, it would have been a much darker ending with the last image being all the Solomans dead in their car lol

As trial lawyers like to say, there isn't a scintilla of evidence that the Solomons "infected" or otherwise appropriated existing Earthling (human) bodies.

I do have the DVDs, but I can't recall the Lithgow comment you mention. Either he knows something viewers don't, or he's unclear on the concept.

The DVD releases don't have commentary from the production team, and I've never come across detailed background information from the writers' room. So I don't know if they went into specific details about the physical transformation from alien to human (and vice-versa) when creating the working "bible" that describes and explains the characters' background.

But my impression is that they created their human bodies from scratch, and picked out features from something like a catalogue or showroom (or perhaps like a web page).

The bodies are real flesh-and-blood, but temporary containers. That's true of real humans, too, but I mean that they were more like shells or cocoons that they simply shed when it's time to revert to their original "purple tube" state.

The fact that Dick uncannily resembled Mary's Sixties professor "friend" was a fluke. Or maybe the alien shapeshifter program was like Google, and compiled body types by secretly surveilling planets and collecting visual records of the inhabitants over many years, and Dick happened to pick the professor's features.

As I recall, they sort of play with the conversion idea; on the one hand, each Solomon chose their human body. On the other hand, they wind up being perplexed and confused with the outcome, from Sally's sweaty boobs to elderly Tommy winding up as a teenager. But they never even suggest that they somehow just popped into existing people, alive or dead.

It's just my guess, but I don't think the writers wanted to tap in to the frequently-used sci-fi/horror theme of predatory, parasitic aliens taking over existing human bodies; this is the stuff of "The Puppet Masters" or "The Father-Thing", but it's too dark and grim for a sitcom like "3rd Rock".

Here is the way I understood it. The aliens had bodies made for them based on humans that were already on the Earth. The reason I think this is because of the episode where Mary thinks that Dick is someone she knew from her past. Then Dick goes home and fusses at Tommy for not researching their parts well enough. I may go back and re-watch the episode, but at the time I got the impression that he simply looked liked that guy.

Like the aliens picked out their bodies like I would pick out a coat at a store, and then I would be wearing a coat that looked like someone else's coat. For them, though, they never actually expected to meet anyone who had known the bodies they had chosen-what would be the odds?

Another reason I got that impression is because a reference was made to Sally picking out her body from a catalog.

In the first episode when the aliens are just arriving on earth and sitting in their car Dick asks if they are all fully formed.

There was another reference when Dick did not want Mary to leave to go somewhere Sally said something along the lines that they still had extra flesh in the freezer and they had the technology to make a new Mary.

All of these indications made me think their bodies were formed from scratch.