There is no combat here.
Basil is located top left. Wares include certain tier-appropriate pickups and a vitapod. Basil has recipes for sale in most mission lobbies.
A place to gear up.
The Vile Engine's lobby is exactly the same as other standard lobbies, with the exception of Basil's inventory.
Map of the standard lobby.
A player's Ready Room.
The standard lobby is a zoomed-out Ready Room.