They don't hold Lyft because of their dual-class share structure.
Yes, Vanguard will buy at "any price" and will buy more at a higher price -- the funds try to replicate the breakdown of the underlying indices on a market cap basis.
If it falls within fund's target they should just buy it, without thinking. That's the point of low cost ETFs.
There's even a known arbitrage opportunity with things like S&P500. When the S&P committee decides to include a new stock (and delist some other stock) you can front-run the purchases by the giants like SPY or VOO, slightly inflating the stock's value just when the ETFs buy it from you.
I doubt this is true, at least not across their primary stock market index funds. For example, VTSAX only holds about 3500 stocks [0].
I don't know how the fund usually treats new, large IPOs, but I highly doubt that they would just blindly buy it at "any price"
EDIT: I just checked the holdings of VTSAX [1] and VGT [2], neither holds Lyft.
[0] - https://investor.vanguard.com/mutual-funds/profile/portfolio...
[1] - https://investor.vanguard.com/mutual-funds/profile/overview/...
[2] - https://investor.vanguard.com/etf/profile/portfolio/VGT/port...