This can be tested and replicated. Simply equip a one handed tool and an offhand item that increased magick power (like a lantern). Look at your magick power stat in your inventory. Now start a spell animation but do not commit the cast. Open inventory, and the bonus is no longer reflected. This leads one to believe that the lantern is never actually applying all it's bonuses at the time of casting. (Update: I left this post to mull while testing, and it turns out that this is a UI bug only. The bonus stats are in fact applying. This was tested using damaging spells on one handed tools both with and without an offhand item. The bonus DID apply to the spells.)
thanks for testing that out! I was about to be pretty grumpy that all that magic I put into my offhand was going to be wasted lol.