Pre-heat oven to 225 degrees and begin heating water for pasta in order to start boiling Linguine about the same time you start the Piccata sauce.
Butterfly chicken breasts, flatten to about 1/2" thickness and slice into cutlets. There is no perfect way to do this, I try to make them somewhat even in size and thickness but each piece will be unique and that's ok!
Salt and pepper the chicken on each side and allow to sit for 5 mins on the cutting board. While the chicken is resting, heat a large saute pan to medium heat and add the olive oil.
Dredge the chicken in flour then pan fry for about 3-4 minutes on each side. When fully cooked, place chicken on a dish and place in warm oven on until ready to serve.
Slice 1/2 lemon into then slices removing any seeds. Juice the remaining 1 1/2 lemons, you should have 1/4 - 1/3 cup of juice.
Leave the bits from the chicken in the pan and add the chopped garlic to the over medium heat stirring occasionally for about 1 min until fragrant. Add chicken broth and bring to a slow boil, then add lemon slices. Allow to slow boil on medium to medium-low for about 5 mins stirring occasionally. The sauce will reduce and slightly thicken.
Add the pasta to the boiling water as Linguine will take about 10 mins and we want the pasta to be done just after the sauce. If using a different pasta, follow the directions adding to the water in order to time the pasta being al dente just after you complete the sauce.
After the sauce has cooked down add lemon juice and capers and allow to cook another 5 minutes stirring occasionally. Add 3 tbsp of butter and stir until fully melted and mixed in. Remove from heat and set aside.
Remove pasta pot from heat, drain pasta, return to the pot and add 2 tbsp of butter. Mix throughly.
To serve, add pasta to each plate with 2 cutlets then cover with sauce and a slice or two of lemon (for garnish).