The New option in the lookup fields for community users does not open the new record creation page for the SFM Lightning Delivery screens. Instead, the object home page is displayed. The behavior of the New option for lookup fields for community users is as follows:

The community user can click the New button to launch the new record creation page as shown in the following screen.

The community user first has to click the New button to launch the lightning home page for an object and then click the New button to launch the new record creation page as shown in the following screen.