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In this work, the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation is investigated. Hirota's bilinear method is used to determine the N-soliton solutions for this equation, from which the M-lump solutions are obtained by using long wave limit when N is even (i.e., N = 2M). Then, taking N = 5 as an example, we discuss some novel mixed lump-soliton and lump-soliton-breather solutions by using long wave limit and choosing special conjugate complex parameters from the five-solitondoi:10.1186/s13662-019-2271-5 fatcat:f4qzmja7fnb3riwcskfgfpeorm