I often print BW on a Lambda with colour material. Either, Kodak N surface or onto Kodak Metallic. Black and white looks ok on colour material depending on the subject and quality of the file.
The main problem I have with printing bw on the Lambda is keeping the bw image neutral. A fluctation in RA4 chemistry temperature will produce a colour cast. Another factor is time between running a control strip and running the final output. Some labs may run a control strip a few time during a printing shift. Others may run their strip at the beginning of the shift and not run another on for the rest of the day or until the roll of paper is changed.
That being said, if you choose to go this route, tell the lab you expect neutral prints.
_harry.