A lance for a burner includes an innermost conduit defining a first fluid passage and a plurality of first fuel injection channels, each first fuel injection channel terminating at a first outlet; an intermediate conduit circumferentially surrounding the innermost conduit, the intermediate conduit defining a second fluid passage and a plurality of second fuel injection channels, each second fuel injection channel terminating at a second outlet; an outermost conduit circumferentially surrounding the intermediate conduit, the outermost conduit defining a third fluid passage, a plurality of third air outlets through the outermost conduit and surrounding the first outlets, a plurality of fourth air outlets through the outermost conduit and surrounding the second outlets, and a plurality of cooling microchannels; wherein each cooling microchannel includes and extends between a microchannel inlet in fluid communication with the third fluid passage and a microchannel outlet on an outer surface of the outermost conduit.