Add sliced rhubarb, 3 tablespoons sugar and water to a medium saucepan over medium heat. Cook, stirring occasionally, until the rhubarb is tender and starting to fall apart (5 to 6 minutes). Pour the mixture through a fine-mesh strainer into a clean bowl. Reserve the rhubarb solids for the cake. Return the liquid to the saucepan and increase the heat to medium-high. Reduce mixture to just under 1/4 cup liquid (9 – 11 minutes). Keep an eye on this as it can bubble over. Reduce heat as needed. Reserve liquid for the whipped cream, storing covered in the fridge.
Preheat an oven to 350°F and set an oven rack to the middle position. Lightly butter a 9 by 13 baking dish and set aside.
In a medium bowl, whisk together flour, baking powder and sea salt. In the bowl of a stand mixer fitted with the paddle attachment, beat eggs, 1 cup of sugar and vanilla on medium-high speed until pale yellow and very fluffy (about 10 minutes). Add half of the flour mixture, and beat on low until just combined. Gradually mix in the milk on low, then the remaining flour mixture. Using a spatula, fold in the cooled rhubarb solids.
Scrape the batter into the prepared baking dish, and bake until lightly golden on top and a toothpick inserted into the center of the cake comes out clean (25 - 30 minutes). Transfer to a cooling rack, and let cool for 30 minutes.
Meanwhile, whisk together half and half, evaporated milk and condensed milk in a medium bowl. Measure out 3 cups for this recipe, and save the rest for another use. Once the cake has cooled, poke holes all over with a fork. Gradually pour the milk mixture over the cake. If it starts to pool, stop and let the liquid absorb before adding more. Cover and let rest in the fridge for at least 4 hours or overnight.
Right before you are ready to serve, make the whipped cream topping. In the bowl of a stand mixer fitted with the whisk attachment, beat together heavy cream, confectioners' sugar, lemon zest and reserved rhubarb syrup on medium-high until soft peaks form. Spoon most of the rhubarb whipped cream over the tres leches cake and spread out in an even layer. Top with sliced strawberries. Serve with any extra rhubarb cream on the side.