I'm raising fund 2. Many institutional LPs (including FoFs) will only invest in $50m+ funds. We'd like those investors in this fund. What amount should we start with in our thesis?

I recommend that you don't reverse engineer like this. This is a trap that many emerging managers fall into. The managers that have done this who we have worked with regretted it when they came in severely under-subscribed because they set a high target since LPs that gave them this objection. This objection is a No, not that if you had a bigger fund they would invest.

We recommend that you set the target to what you can realistically close relatively easily in the next 18 months. First, asses the LPs in Fund 1. Typically ~70% often re-up in Fund 2s. Then, review the relationships you have built with other LPs over the years that you think have a realistic shot at closing. Let's say that after this exercise, you feel very comfortable reaching a $15m target.

Consider then setting the target in the $15 - $20m range max. Then, if/when LPs of the archetype that you describe give you that objection, say something like this in your own words:

"Our target is $[x], and we are confident that we will likely over subscribe. What is your process from here on out?"