Worth mentioning that given the current cheap money, a lot of the investment is leveraged, on credit or timed. So you don't have to have 2m sitting idle in a bank to lead a round.
I imagine each VC fund has a multitude of LPs and they each manage cash based on their own strategies. The key is that they have enough liquid assets to meet the obligations in a timely manner.
Obviously, each fund is set up separately and might have a different structure.