It is possible to use a lantern while it is in the player's active item slot (cursor picked) while also having an item in their hands to use.
Basically the lantern will still be on and the player is able to attack with a weapon.
Drop wanted hand-based item on the ground. Put lantern in hands. Click to pick up item, and while moving towards the item click on the lantern to put the lantern in the active item slot. Player will continue to go pick up the item on the ground and auto-equip it in the hands slot. Lantern is still active and player is able to use the item in hands slot freely.