Cream shortening or butter in a stand mixer fitted with a beater attachment or with a hand held beater.
Add 1/2 of sugar, salt, lemon juice and zest, and vanilla. Beat on low gradually increasing the speed. Add all of coconut milk and continue beating. Then add remainder of sugar and whip until smooth and creamy.
If mixture seems too dry add a splash more milk, if it seems to wet add a bit more sugar until you reach the desired consistency.
Use an offset spatula to spread buttercream onto bottom layer of cake. then place second cake on top. Spread more buttercream on top and sides of cake. Use edge of offset spatula to scrape away frosting from the sides for the "naked cake" look. Enjoy!
Recipe by Fare Isle at https://fareisle.com/vegan-carrot-cake-with-lemon-buttercream-and-fresh-figs/