Q:

Is Aunt May friends with Doctor Octavius?

When Hobo-Spidey and Miles infiltrate the Alchemax laboratory out in the forest, they inadvertently come face to face with Dr. Octopus, who in this dimension is actually a female version, Dr. Olivia Octavius.   In the screenplay it reads:

HEAD SCIENTIST
My friends actually call me Liv.
(then turning)
My enemies call me Doc Ock.

When all the Spiders are grouped up at Aunt May's house and attacked by Doc Ock and her cronies, Aunt May says:

DOC OCK
Cute place. Real homey.
AUNT MAY
Oh great, it’s Liv.

So if only friends of Doc Ock call her Liv, and Aunt May calls her Liv here, is it safe to say that Aunt May is a friend of Olivia? It seems somewhat possible, considering she also acts as a pseudo-Alfred for Spiderman, what with themed cars, a myriad of suit colors and choices, and many technological upgrades.

A:

There's a suggestion that this is a throwback to deeper Spider-Man lore from the comics like some of the other references and jokes. 

In the video above MovieBob talks about how in the Spider-Man comics there have been instances where Doc Ock and Aunt May have had a thing for one another. At the start it was Aunt May working for Doc Ock as a maid, seeing him as a good person and Spider-Man being a bully to him and later (after getting out of prison) Doc Ock dates and goes to marry Aunt May, though this was a scheme to get access to a nuclear power plant on an island Aunt May unknowingly inherited Doc Ock grows to care for her and doesn't want her hurt as apart of the scheme. 

^ Spider-man Issue #131
After this MovieBob also mentioned that Marvel has revisited this relationship in the comics indicating Doc Ock and Aunt May had chemistry and may even be hooked up.
How does this relate to Into the Spider-Verse? Well before the timed part, MovieBob suggested they could have been scientists together but there are other throwaway Easter eggs that are for the more devoted fans of the comics who would know about and Doc Ock and Aunt May being a couple would be one of them. 
As such MovieBob's opinion is that Aunt May may not be just friends with Doctor Octavius, they could be former lovers, and in that context "Oh great, it’s Liv." does sounds like something someone would say when their ex suddenly appears. *internally screams like a girl for yuri*

