While family inventory can't be used, personal inventory can be. You can drag relics, gems, paintings and photographs out of your inventory and place them on public lots (I'm not entirely sure if you have to own that lot or not, but any time I do this, my sims do own it). This, of course, leaves statues out...but this can be rectified by placing a sculpting station on the lot and sculpting the statues on site. You can then use the real estate build/buy option to place the statue where you want. However, an on-site sculpting station has acted a little weird for me at times, and it doesn't want to let me start sculpting sometimes.
It's worth mentioning that artworks placed on public lots do not appreciate in value.