Canon is mostly silent on the lives of low-rated telepaths, which is sad because their stories are also interesting (and this project will get a little into this topic later). Some of these folks, like Lyta's mom, were born in the Corps, but never developed telepathy strong enough to be formally attached (her mom was a P2). Others are born to normal parents, and must be registered as telepaths, but are afforded none of the social protections of telepaths in the Corps (housing, employment, health care, etc.). They fall through the cracks because on one hand, the registration laws are set by the EA, while on the other hand, the Corps promulgates its own regulations as to the cut-off rating. From their point of view, it's not worth the resources to train telepaths who are not strong enough to work "as telepaths" in the few professions telepaths are permitted to hold. They do monitor these telepaths (once or twice a year) to see if their abilities have strengthened - and sometimes, they do, especially with children - but after a certain point, you are what you are.
To be clear, Ivanova is not in this category - she's not even a P1. She's what's called a "latent" telepath, meaning someone who is legally a normal but who has some trace telepathic ability. These children might have a telepath parent and they might not.
It's super rare (to the point of unheard of) for two telepaths to have a child who is actually a normal, but it's not uncommon for telepaths (especially on the weaker end) to have children who don't rate highly enough to be in the Corps. These children will have started life in Psi Corps schools with their telepath peers, and, like all telepath children, will probably be in their teens (or even sometimes older) before their abilities develop and they get the shock that they can't be in the Corps. Lyta's mom developed telepathy early, at eight years old, but as a P2, she could no longer attend the Corps school in Geneva, and her mom (Natasha Alexander, of Department Sigma... a very important figure) arranged for her to live with relatives outside Teeptown. Telepath relatives, we can safely assume. But at that point she drops out of the picture, because she wasn't in the Corps. Canon, which meticulously names everyone else in Lyta's matrilineal line back six generations, leaves her mother out. Lyta briefly speaks of her mom, but never names her, and appears not even to have known her.
We know is Lyta, herself, was raised in the Corps like her mother and grandmother, and developed telepathy very early (before age seven), which is how she got to be in the elite "Cadre Prime" (that and her connections through her grandmother!). It appears she developed her powers even younger than that, since she spend no time in the dorm for "latents" (defined differently here than everywhere else, here as children who didn't get telepathy especially early), and seems to have been placed in her cadre right from the start (age 6, which is 5 in telepath age reckoning).
(Some folks in fandom confuse the date on her commercial license as the date she joined the Corps. No - this is the date her license was issued, when she completed training. Commercial licenses are renewed every ten years.)
What of these children who can't attend telepath schools? Canon doesn't say. What of the teenagers or even young adults who find out that they can't be in the Corps, and they must take off their gloves and live "in the normal world" that doesn't want them? And what of the children from normal homes, who still face all the discrimination of being a telepath, even though they can't be in the Corps?
To those in the Corps, these people are "not full telepaths" and so in a sense, they "don't count," while to those in the normal world, a rating is a rating, and everyone has a really hard time understanding how someone can have a rating and not be in the Corps (and an even harder time understanding how someone can grow up in the Corps and then not be allowed to be in the Corps as an adult!). If you're a telepath, you're not a normal. These children (and adults) find themselves unwelcome in both worlds.
In telepath culture, there's also quite a bit of emphasis placed on having children who rate the same as or higher than you, and who can "advance" in the Corps. If children rate too low (e.g. below the threshold to be in the Corps), parents may blame themselves, and if they are traditionally-minded, may even split up to marry other people and try again (or at least try for higher-rated children through IVF). That Lyta's mom isn't named, I think, really says it all.
As a final note, I will point out that in Crusade we learn that P1s and P2s (at least those with useful skills, such as medical training) were drafted in the Corps during the Crisis. This makes sense - the cut-off rating was always defined on the Corps' side, not by normal law, and during the Crisis, they really needed All Hands On Deck. While low-rated telepaths raised in the Corps might be glad for the chance to redeem themselves in the eyes of the telepath community, those raised outside the Corps might be very unhappy about this change in regulations.
But more on that when we get there.