Can I solubilize lemon essence in water somehow?
Some hints are provided by Wikipedia:Lemon liqueur:

To produce the Lemon liqueur requires sugar, water, lemon zest,
mixing in organic salutes  liquor, and time to mature. Lemon zest is soaked in high proof neutral spirits to extract from it the lemon oil (an essential oil). The extraction is then diluted with simple syrup.

In other words, lemon zest is drawn into water by mixing in water-soluble organic compounds, in this case sugar and (ethyl) alcohol.  If you want it to be nonalcoholic, maybe just the sugar will do.
During late autumn I make a cranberry jam by boiling the cranberries with oranges, sugar and water.  In the presence of the sugar and organic material from the oranges and cranberries and with the application of heat, orange zest is extracted into the jam.  The jam is too dark and thick to see whether the zest remains in solution when the jam is cooled, but the extraction of the zest is evident by taste.