Under investigation in this work is a newly proposed nonlocal long-wave-short-wave resonance interaction (LSRI) equation with the self-induced parity-time (PT) symmetric potential. This equation offers PT symmetry analogues of the classical integrable LSRI equation and may be important for the occurence of such equations in nonlinear optics as the nonlocal NLS equation. General soliton solutions to the nonlocal LSRI equation with nonzero boundary condition are derived by using the Hirota's bilinear method combined with the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are expressed in terms of Gramian determinants and include dark-dark solitons, dark-antidark solitons and antidark-antidark solitons. Three typical cases of the two solitons, namely two dark-dark solitons, two dark-antidark solitons and two antidark-antidark solitons, are demonstrated.