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Make cake layers:.
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Put oven rack in middle position and preheat oven to 350u00b0F Brush cake pans with canola oil. Line bottoms of two 9-inch round cake pans with a round of parchment or wax paper, then oil paper.
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Whisk together flour mix, salt, baking powder, and xanthan gum until combined well. Stir together milk, canola oil (1 cup), vanilla, and zest in another bowl.
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Beat together sugar and eggs in a large bowl with an electric mixer at medium speed just until combined, about 1 minute. Reduce speed to low and add flour and milk mixtures alternately in batches, beginning and ending with flour mixture and mixing until just combined.
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Divide batter evenly between cake pans, smoothing tops, and bake until a wooden pick or skewer inserted in center of each cake layer comes out clean, 35 to 40 minutes.
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Cool cake layers in pans on racks 10 minutes. Run a thin knife around edge of 1 cake layer and invert rack over cake pan, then invert cake onto rack. Repeat with second layer. Peel off paper and cool layers completely.
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Make curd:.
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Whisk together zest, lemon juice, sugar, yolks, a pinch of salt, and guar gum in a 1-quart heavy saucepan. Add butter and cook over moderately low heat, whisking constantly, until curd is thick enough to hold marks of whisk and first bubbles appear on surface, about 5 minutes. Whisk in extract. Immediately pour curd into a bowl, then cover surface with wax paper and chill until cold, about 30 minutes.
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Make frosting:.
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Beat butter with an electric mixer at high speed until light and fluffy, about 1 minute. Reduce speed to low and add confectioners sugar, lemon juice, extract, and zest, then mix until creamy and smooth, about 2 minutes.
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Frost cake:.
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Halve each cake layer horizontally using a long serrated knife. Spread bottom half of each cake layer with half of lemon curd, then top with remaining cake layers to form two sandwiched cakes. Put 1 sandwiched cake on a cake stand or platter and spread a heaping 1/2 cup frosting over top, then cover with remaining sandwiched cake. Frost top and sides of cake with remaining frosting.
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Cooks' notes:.
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Cake layers can be made (but not halved) 1 day ahead and cooled completely, then kept, wrapped well in plastic wrap, at room temperature.
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Lemon curd can be chilled up to 3 days.
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Cake can be completely assembled and frosted 4 hours ahead and kept at room temperature, or 1 day ahead and chilled, loosely covered. Bring to room temperature before serving.
