In a small, cool saucepan, mix together egg yolks and sugar. Add lime and cucumber juices to pan and stir to combine. Cut softened butter into small chunks and add to mixture. Add food coloring, one drop at a time, mixing after each drop for a light green coloring.
Over med heat, cook filling, stirring constantly to ensure a smooth texture. Heat mixture until it thickens and coats the spoon/spatula; do not boil. Pour hot mixture over crust and cool completely. Slice into squares and serve.
*Use a juicer to extract juice from peeled cucumber, or macerate in a blender and squeeze through a cheesecloth, ensuring that no cucumber chunks make it into the mixture.