Answer: Sounds like some creepy crawly critter has decided to take up residence in the potting soil. As you've discovered, spraying a fungicide won't be effective against insects - but it will kill fungus. It's always a good idea to read the label of any product before use to make sure it is safe to use on your plants, against the problem you are trying to control.
Since we don't know what these pests might be I think you can control them by simply placing a temporary barrier atop the soil. This way the critters won't be able to get light or fresh air and I think they will die off on their own. Use plastic wrap, foil, or a layer of decorative rocks as a barrier.
If you're finding sticky leaves, closely examine the undersides of leaves and the stems for signs of insects. When they feed they exude a sticky substance called honeydew. If things are sticky, I think you'll find aphids, whiteflies, scales or mealybugs feasting on your plant. If you find them, hose them off, rub them off, or treat with a registered insecticide.
Best wishes with your lemon tree!
Q&A Library Searching Tips