Yes, you can absolutely send a 1-pager with fund details to an LP who requests it. This is a common practice in fundraising.

A one-pager is often useful when someone expresses interest but isn't ready for a full pitch deck or formal meeting. It should include your fund thesis, key investment parameters (stage, sector, geography, check sizes), your background/competitive advantage, and basic fund terms.

Just keep in mind that if you're raising under 506(b), you should only send materials to people you have a pre-existing relationship with or who specifically request information after learning about your fund through those relationships (not from public solicitation).