Preheat oven to 325˚F.
Combine coconut, finely chopped walnuts, vanilla, milk, and honey in a bowl, mix well until thoroughly combined and set aside. Mixture should be just moist. If it looks too dry, mix in couple more tablespoons of milk.
Grease a jellyroll pan with melted butter. You can also use a 9x13 baking pan, but you will have to cut the phyllo sheets to fit.
Unroll the phyllo sheets; as you work with the phyllo sheets, keep the sheets covered with a damp paper towel so they don’t dry out. You can also use plastic wrap to cover the stack.
Layer 10 pieces of Phyllo sheets inside the pan, brushing each sheet with melted butter before adding the next.
Sprinkle about ¾ cups of the coconut mixture over the layered phyllo sheets.
Continue to layer 5 more phyllo sheets, brushing each sheet with butter before adding the next.
Sprinkle with more of the coconut mixture. Repeat with 5 more sheets of phyllo and sprinkle with coconut mixture again; repeat this 2 more times. See my Notes below for how to layer the phyllo sheets.
Finish the baklava with a layer of 10 phyllo sheets - brushing each sheet with butter - and finally, brush the top with more melted butter.
Cut the baklava. First, cut it into 4 long rows, and then cut diagonally to make diamond shapes. You can also cut straight across to make square shapes.
Bake for 55 minutes, or until golden on top.
Remove from oven and let completely cool.
In the meantime, prepare the syrup.
Combine water and sugar in a saucepan and bring to a boil; lower heat to a simmer, and continue to cook for 15 minutes.
Remove from heat and stir in the lemon juice.
Pour the hot syrup over the completely cooled baklava. OR, you can pour cold syrup over hot (just baked) baklava.
Let stand in a cool dry place, uncovered, for at least 6 hours or overnight.