Preheat the oven to 175C. Butter and flour 8x8x2 inch (lined) baking pan. (I used a medium size bundt pan and sprayed pan with cooking spray).
Sift self-raising flour into a bowl and mix with black chia seeds and lime zest, set aside.
Using electric mixer, beat butter and icing sugar until well blended. Beat in eggs one at a time. Beat in milk, mix well. Add in flour mixer and fold well with a rubber spatula.
Transfer batter to prepared pan; smooth top.
Bake cake until tester inserted into center comes out clean, about 33 minutes.
Meanwhile, finely grate enough lime peel to measure 1 tablespoon. Halve limes, squeeze enough juice to measure 3 tablespoon. Stir lime peel, lime juice and 3 tablespoon sugar in a small bowl until sugar dissolves. Set lime syrup aside.
Once cake is done, remove from oven and let it stay in cake pan for 5 minutes. Remove cake and immediately brush lime syrup generously on the surface.
Cool cake completely and serve.
Recipe by Anncoo Journal at https://www.anncoojournal.com/lime-cake/