Plasmonic surface lattice resonances (SLRs) supported by metal nanoparticle arrays exhibit narrow linewidths and enhanced localized fields and thus are attractive in diverse applications including nanolasers, biochemical sensors and nonlinear optics. However, it has been shown that these SLRs have much worse performance in a less symmetric environment, hindering their practical applications. Here, we propose a novel type of narrow SLRs that is supported by metal-insulator-metal nanopillar arrays and that has better performance in a less symmetric dielectric environment. When the dielectric environment is as asymmetric as the air/polymer environment with a refractive index contrast of 1.0/1.52, the proposed SLRs have high quality factors of 62 under normalincidence and of 147 under oblique incidence in the visible regime. We attribute these new SLRs to Fano resonance between an in-plane dipole and an out-of-plane quadrupole (or dipole) that are respectively supported by the two metal ridges under normal (or oblique) incidence. We also show that the resonance wavelength can be tuned by varying the geometric sizes or by changing the angle of incidence. By doing this, we clarify the conditions for the formation of the proposed SLRs and illustrate their attractive merits in sensing applications. We expect that this new SLR can open up applications in asymmetric dielectric environments.