This is what I found on the internet. You did say the rust was right at the edge of the fabric. Nowhere near the embroidery. I wouldn't put lemon juice anywhere near my embroidery area, because I reckon it will change the color of the fabric.
I'd also tape the area of affected fabric over a glass bowl or something, to make sure non of the rust remover stuff gets anywhere near the rest of the fabric when applying or rinsing it.
Instructions for Removing Rust Stains
First, do not make the stain worse by applying chlorine bleach as this will react with the rust and may intensify the discoloration.
Remove as much of the rust stain as possible before applying a treatment.(Sandpaper may help here).
Follow the instructions on the package if you are using a commercial rust removal product.
Squeeze lemon juice onto the stain so that the spot is thoroughly saturated.
Sprinkle salt onto the lemon juice.
Allow the salt and juice to react with the stain for 24 hours. Refresh the lemon juice to keep the spot damp.
Blot the stain (do not rub, as this may damage the fibers).
Rinse the spot with cool water. You may repeat the process, if needed
Another method is to apply a mixture of 1/4 teaspoon mild liquid dish soap in one cup warm water. Thoroughly saturate the stain and allow the solution to react for at least 5 minutes. The surfactants in the detergent will help to lift the rust particles.
Blot the stain with a clean white cloth or paper towel and rinse it with cool water.
Repeat this process until the stain is removed or until no more discoloration is picked up by the cloth.
Thoroughly rinse the spot with water to remove all traces of cleaning solution.