Amy R
Wild question - I would browse grills and smokers on ebay and see what looks familiar, or if it is more recent vintage, you could just browse them on the internet or even walk through your local lawn shop or home improvement store and look for the same thing. But first I would look at the hardware near the handle for a logo or name and look at the plate (if there is one) near the operators or the connections (if it is gas or propane) and see if the manufacturer or model number is there. Normally, there is a logo on the lid, or the underside, or the hardware, or the interior of the cabinet.