Okies, here is what you do. Next to the vendor who has a lantern hat, place a square goza mat. Raise it up two times. Unlock and grab the lantern. Stand outside the plot and check the vendor inventory with the vendor owner. This will move the vendor outside and leave a little red plaque on their tile.
Now place three small wooden tables on top of each other on that plaque. You need to be standing on the square goza mat that has been raised two times, then place the lantern on the top table and lock it down. Remove the middle table first, then the other two tables.
The lantern is actually too high now if it is inside the house (outside is fine) - it will poke thru to the floor above. Use your int dec tool to lower the lantern once and that should fix this. Now it should be hovering just over the vendors head.
If you have problems with this I can meet you ingame and we can get it sorted out!
Short directions:
1. place square goza mat on tile next to lantern tile and raise it 2 times
2. remove vendor by stepping outside the plot and looking at their wares (can use their healthbar to get the menu)
3. place three tables on the lantern tile and stand on the square goza mat
4. place the lantern on the top table and lock it down
5. remove the middle table first then the other two, chop goza
6. lower lantern 1 time if you are indoors
Issues you might have could stem from having other deco on that tile, which will make things go too high to place everything, so it needs to be clear of deco if possible. Anything that is ground level or thereabouts can be replaced after you lock the lantern down and move the tables.