Answer: Lemon trees usually adapt well to growing indoors so I think the symptoms you are describing are a result of the scale insect infestation. Scales feed on the fluids within the tissues of the plants and a large number of the pests can really stress it out. All that sticky stuff is essential to the tree and having it run down the outside means it is not being transported to the leaves and stems as it should be. Your first course of action is to rid your plant of the scales. There are chemical sprays (look in the houseplant section of the garden center) or you can peel each one off, or you can dab them with a cotton swab dipped in rubbing alcohol to kill them.
Like most houseplants, citrus thrive in a normal household temperature range of 70 degrees during day, to 55 to 55 degrees at night. Citrus trees prefer full sun from a southern exposure. If that's not possible, you can supplement the light by installing 40-watt fluorescent shop lights above the plant, keeping it on 14-16 hour a day. As for moisture, you'll need to keep the soil evenly moist and since most interiors are quite dry during the winter months, mist your plant often -- daily if you can. Give your lemon tree a shower occasionally to remove dust. Browning fruit indicates inadequate soil moisture so adjust your watering schedule, provide adequate light, and your tree should stop losing leaves and begin producing healthy new leaves and flowers. Best wishes with your lemon tree!
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