Three months ago, I brought a 5-foot ficus tree to a similar non-direct lit area indoors. One month ago, leaves started to drop, and I noticed ones on the plant were sticky to the touch. Six months ago, while still outside, I repotted in a 16-inch pot with a hole for drainage, and no water has ever appeared on dish below it. It was healthy on the shady north side of my home in a 10-inch plastic pot for five years prior to the repotting into a good, moisture-control potting mix.
Ficus are sensitive when moved to a new location, and they often show their unhappiness by shedding leaves. As long as there isn't a draft in the new spot, they'll settle down and releaf.
The stickiness you describe, however, is bad news; it sounds like honeydew -- the waste of sap-eating insects like spider mites, scale, or mealy bugs. Scale and mealy bugs are visible on the plant. Scale look like little gray or brown bumps. Mealy bugs look like little white cottony masses. Spider mites are so tiny that you can't usually see them, but you might see webs or feel a gritty feeling between your fingers if you wipe them along leaves and branches. If it's scale or mealy bugs, buy a houseplant insecticide at the garden center, and apply it according to the label.
You can also dab the insects individually with a Q-tip dipped in rubbing alcohol, but I've found that to be overwhelming on large plants. If it's spider mites, take the ficus back outside and wash it thoroughly (tops and bottoms of the leaves, all branchs and the trunk) with a strong blast from the garden hose. Spider mites are so tiny and vulnerable that a harsh blast of water will kill more than 90 percent of them.