

Luckily, people research these things.
Apparently the Voyager crew used the Thermos Nissan Vacuum Insulated Espresso Mugs, models JMJ-180 (a smaller one used by various crew members) and JMJ-185 (a larger one favored by Janeway). Apparently these did come with a lid.
There’s a reason why oldschool X-Com players kept coming back to the games despite technical issues like the Groundhog Day bug. (Thank all applicable deities for OpenXcom solving those issues, though.)