You could be describing my sister who I am now Nc with and this was one of the reasons.
Total drama queen, always playing "one upmanship" but with tragedies as well as successes.
Constantly "reinventing" herself depending on what "bestie" she's cultivating at the time - she does this thing where she's "besties" with someone, gets jealous if they spend time with anyone else (including partner/spouse) but she selects them based on what they can do for her - usually materially - and to develop the relationship she goes somewhat SWF on them.
Over the years she's been "earth mother" (despite being completely flaky as a parent and frequent palming the kids off on others especially my mum, one time she asked me to babysit for a fri night out, she didn't answer her phone until noon on the Sunday and didn't collect the kids until teatime - and then lost it with me for giving the kids dinner!) "career woman" (despite never having held a job for more than 2 years Max, usually 12-18 months), "airhead blonde" (despite being well educated and intelligent), "sporty mum" (despite hating exercise of any kind)
She's lied about ridiculously trivial things like how she takes her cuppa tea or what she's had for lunch, to really quite serious, disturbing things including serious illness of her or DC, pregnancy "scares" etc
The stuff with DCs health has really messed with my mums head, mum takes the stance of always believing her as she'd hate to not and not be supportive of dgc suffering but it's infuriated me! Having me worried sick about a Dn only to find out it was yet another self created drama of hers.
She does have mh issues as do I, but I don't think that's an acceptable excuse for the heartache she's caused and continues to cause, and I believe it's also meant she's lovely been misdx and therefore not received appropriate treatment.
As I say I'm Nc with her now, partly due to more lies she told about an assault she made on me which were thankfully disproved by cctv.
So I think it's a mistake to dismiss these sort of people as "harmless" they aren't always, especially in a work environment.
I would advise cautiously, gently making it clear to the op's liar that op knows X was a lie and taking any potentially harmful lies straight to management.
I know my sister has caused problems for colleagues and employers if they've "wronged" her - that's a large reason why she can't hold down a job!
I've had people from our past come to me with the most ridiculous things they believed to be true of her or me or our family that they totally believed and are shocked to learn weren't true.
The SWF stuff I've found out have been quite shocking too and includes making inappropriate comments to and plain making passes at supposed friends partners/spouses. Claiming that they've made passes at her (usually when she's wanting something out of that couple/family and the partner/spouse has started to get wise to her and advising that "bestie" to be cautious, so she's trying to discredit them)
Whatever the reasons, completely unacceptable behaviour.
"Sometimes people like this lie about their own competence to the extent that they get trusted with a job they can't do, with awful fallout." My sisters done that, lied about qualifications she'd never even studied for! Was soon discovered but was a nightmare for the company concerned, but then partly their fault for not doing their due diligence and checking!
It's not always harmless and it does naturally make you less likely to believe them when they are telling the truth - which is also awful, because if they lie eg about a serious illness and you don't believe them and then they end up very ill/in hospital etc you feel shit for not believing them even though it's their actions which caused you to be disbelieving.
Easy for those who haven't experienced it to this level to be dismissive and judgmental of those of us who have for not being "compassionate" enough. 