I have a 3 years old Lemon plant that I grow from seeds. Some white thing ( like spider nest) appeared on branches and some sticky drops ( honey like) also can be seen on leaves.
Please kindly let me know how I can rescue my plant.
From your picture, I would say your plant has mealy bugs. The adults have antennae and crawl very slowly when disturbed. Eggs and larvae are found in crevices. They appear as white powdery clumps or tiny white specks on the leaves. Mealy bugs suck the sugar-rich sap from all parts of the plant but especially new growth. As the bugs multiply and continue to feed, the plant will eventually weaken and die, however it takes quite a while for the conditions to get that bad. Mealybugs also excrete large amounts of honeydew. This sugary waste becomes colonized by sooty mold causing leaves to look dark and dirty.
If the infested plant could use a pruning you can start by pruning most/some of the infested sections. You can also try to dislodge the pests with a jet of water, either in your shower, sink or with a garden hose outside (when the weather gets warmer). If you just have a few sites with mealy bugs, you can use tweezers to remove them. Mealybugs are more apt to be a problem with indoor citrus trees. Containerized citrus plants can be moved outside during mild weather to spray them with an insecticidal soap. Follow label directions for mixing and spray trees to the point of run off. These sprays are also very effective against whiteflies and aphids. Apply the sprays when environmental conditions promote slow drying (i.e., early morning and early evening). Repeat spray applications in 5 days if necessary. Thorough coverage on the undersides of the leaves and new growth to the point of run-off is especially important when using soap sprays. Do not use insecticidal soap sprays when the citrus is in bloom. The following link has information on many different kinds of citrus pests. Although it is written for the orchardist, the advice applies equally well to those of us who have only a few citrus plants.
Good luck. Since you started this plant from seed, I’m sure you’re quite attached to it.