Generally speaking, yes - this can be done (though the LP may wish to consult a tax advisor).
If the LP has already wired in some capital, an Assignment and Contribution Agreement or its equivalent is typically signed between the LP and the LP's trust. If the LP has not yet wired any capital, it is often easier to have the LP sign a Withdrawal Agreement or its equivalent and then sign the LPA again in the name of the trust (or another name/entity as desired).
Decile Partners has standardized templates for both of the above situations (designed to work with Decile Group's standard suite of templates), and will coordinate to assist Decile Launch customers in completing them. Please contact your Venture Associate to inquire.