If historical authenticity matters in your games, here's the best you're going to get in the way of lanterns in the Middle Ages. And bear in mind it'll probably contain a spitting, smoky, unreliable tallow candle, not wax because those are reserved for church services.
Or you could carry an oil lantern. That's not one of the storm-lamps you see in medieval movies. It's a dish of oil with a wick in it and, if you're lucky, a cover of horn or glass to stop it blowing out. (Argand lamps came much later.)
From the Jewelspider rules:
"Night’s black agents thrive in a world lit only by fire. Even in a wealthy baron’s castle, those ubiquitous flaring torches are a myth; after dark the passages and side chambers are unlit. If you need to leave the main hall, you carry your own sputtering lantern (containing a tallow candle or a wick in a dish of oil) or get a servant to accompany you with a torch or candelabrum. Thick trembling shadows fill the further reaches of the hallways, giving many places for a stealthy interloper to hide."
