I've never used lemon (or lime) juice in RI, but I know many people do. I would try the lime juice and maybe the tiniest bit of orange extract.
I found this recipe here that uses lemon juice.:
http://www.cakecentral.com/cake_recipe-2320-1-Royal-icing-for-decorated-cookies-II.html
So many recipes to try from this site -- so little time! 
I always put lemon in place of some of the water in my RI. It really cuts the sweetness of the icing. Also, its good for masking the bitter taste you get from red icing.
I wonder if giving them a light sprinkling of sea or kosher or margarita salt might help with the sweetness and heighten the margarita experience? I use to bake "margarita bars" that was nothing more than a lemon meringue recipe made with limes (no meringue) and I discovered that making the crust from crushed pretzels incorporated just enough salt to make them believable as margarita bars instead of just lime bars.
I made margarita cupcakes w/key lime icing for Cinco de Mayo...they were awesome!!!
How about a splash of tequila and the fine zest of one whole lime? I do Lime SugAr Cookies for weddings in the summertime and they taste amazing! To make the lime flavour even more pronounced, zest the lime into your white sugar as you gather your ingredients together. Rub the sugar/zest it between your hands to get all those potent oils out and the flavour is really strong! 
Could I use lemmon and lime juice in place of liquid in RI and maybe NFSC to get that margarita taste for a fun summer cookie bokay? (shapes- martini glass, flip flop, palm tree, beach ball, watermellon slice)
You sure can use lime juice. I use lime juice in my royal icing all the time. This is especially true when I make traditional royal icing using egg whites. It's really good.
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