For the caramel, combine the sugar and lemon juice in a small saucepan. Mix well with a metal spoon (a wooden spoon might carry traces of grease, which could make the sugar crystallize as it melts) and place over low heat. At the first sign of smoke, stir occasionally until the caramel is deep golden in color. Add the water, allow to return to a boil, and cool the caramel for about 1 minute.
Pour the caramel into a 1½-quart Pyrex loaf pan and tip the pan in all directions to coat it well. Pour out the excess caramel and allow the loaf pan to cool while preparing the bonet.
For the bonet, preheat the oven to 300 degrees and set a rack in the middle level. Bring the water to a boil in a small saucepan and remove from the heat. Stir in the coffee, cover the pan, and allow to steep for 5 minutes. Strain through a fine strainer into a measuring cup, then line the strainer with a paper towel or coffee filter and strain again. Measure ½ cup of the coffee.
Combine the cream, milk, and sugar in a saucepan. Bring the mixture to a boil over medium heat, stirring occasionally. In a large bowl, whisk the eggs to break them up and whisk in the rum and coffee. Whisk in the boiled cream mixture in a stream.
Pour the mixture into the caramelized loaf pan and set in a pan that contains 1 inch of warm water. Bake the bonet for about 1 hour, until it is firm to the touch and well colored on top. Be careful that the water in the pan does not simmer; add cold water to prevent it from becoming too hot, if necessary.
Cool the bonet at room temperature for half an hour, then cover with plastic wrap and refrigerate.
To unmold the bonet, insert the point of a paring knife about ½ inch deep between the bonet and the loaf pan and, scraping against the pan, loosen it at the top. Invert a platter onto the pan, then invert the pan and the platter. The pan should lift off easily. If it does not, shake gently from side to side so that some air gets in between the bonet and the pan; the pan should then lift off. If not serving immediately, cover loosely with plastic wrap and refrigerate. Serve the bonet in 1-inch slices.