I would like to use a shortbread recipe for making lemon short bread cookies, this recipe only uses sugar and butter and doesn't use any eggs or milk, I was thinking that perhaps I could add lemon extract and use lemon zest do you think it would work?
If the recipe on its own (without alteration) works, your modifications should be safe, mind that an oily extract or coarsely cut zest could have an additional shortening effect.
Be careful with lemon JUICE though, the acidity can change the texture. And avoid putting in other watery ingredients (milk,juices), they will encourage gluten formation and lead to a softer, cakey cookie.
Expect there to be SOME leavening and deformation in the oven if using butter/margarine, since there is still water bound in these fats. So if a perfect "commercially baked" look is desirable, constraining the cookies in molds and/or using different fats might be needed.
Experimentation with different flour grades, and probably with adding pure starches, is a good thing to do once you have made the base recipe work.