Can LPs sell shares in lieu of capital calls?

Please clarify the question - are you asking if a Limited Partner can sell shares that the Limited Partner is holding onto as an individual in order to generate cash to fulfill the Fund's capital call? 

Thanks for your response, Haw. Yes, can LPs sell shares to an individual or other LPs in order to fulfill the fund's capital call? 

Please clarify what you mean by "or other LPs". Thanks. 

"Other LPs" as in the other LPs participating in the fund - for example LP #1 sells shares to LP #2 in exchange for cash

If a limited partner is holding shares of a private company's stock, and wishes to sell them in a secondary transaction to generate cash, as long as they follow the company's legal agreements/procedures and the company consents, this is theoretically possible.  

The limited partner can then use the cash to fulfill a pending capital call to a Fund. If the person purchasing these shares of a private company's stock is also a limited partner in the same fund, I suppose that's possible, though it would be pretty rare. 

Great! Thanks for the clarity, Haw