Well, unless a venue has 0 stars and thus produces no income one does not *have* to upgrade a venue - it *just* maximizes the profit if you do.
Unless there are specific requirements (like need a bench, 2 barbeques, etc.) you only have to sink in enough money to reach the needed amount of lot value to go to the next level - up to level 3, which is max.
As you do not have access to your family inventory you cannot drop expensive statues - but you can drop stuff from your normal inventory like heartshape cut pink diamonds, spire cut and grown Tiberium, self created pictures, etc.
You can also place an easel or a sculpting station in your venue and produce right there then place the end results on the property, thus increasing the value.
If you can't paint or sculpt you gotta buy things like pictures and statues and place them all over the place to increase lot value. Changing the floor and wall coverings and replacing the lamps, adding carpets and whatnot also works nicely. In a classic venue (i.e. not in a skyscraper) you can also add the fish window thingy which is a good boost for lot value - not sure, though, if you can do this in any of the new LN buildings - so maybe you'll have to stick to expensive furniture, statues, pictures, stereo, etc.