An LP asked me: do non-U.S. citizens need to pay estate tax if they invest in a Delaware fund as an LP?

Non-U.S. citizens generally do not need to pay U.S. taxes on capital gains from a Delaware fund as an LP, as capital gains are not sourced to the U.S. and are not taxed there. However, they may need to pay taxes in their home country. Always recommend that LPs consult with a tax professional for specific advice and avoid providing LPs with tax advice. 

Assuming this is regarding when the estate transfers to the decedents. Typically in this situation the decedents basis in the investment gets stepped up to the fair market value of the partnership interest at the time of the transfer. Then they will need to pick up their pro rata share of income/expense as detailed by the K-1 annually. I am not aware of any estate tax charged on a partnership interest especially for a foreign partner. Tax advisor should be consulted.