We study arrays of plasmonic nanoparticles combined with quantum emitters, quantum plasmonic lattices, as a platform for room-temperature studies of quantum many-body physics. We outline a theory to describe surface plasmon-polariton distributions when they are coupled to externally pumped molecules. The possibility of tailoring the dispersion in plasmonic lattices allows realization of a variety of distributions, including the Bose-Einstein distribution as in photon condensation [Klaers et al., Nature (London) 468, 545 (2010)]. We show that the presence of losses can relax some of the standard dimensionality restrictions for condensation.