Rinse the rice and set it aside.
Mince the garlic and shallot and set aside.
Zest one lemon and then juice it. Set aside. You will need one teaspoon of zest and two tablespoons of juice. Thinly slice another lemon and set aside.
Add the olive oil to the inner pot. Press saute to heat up for a couple of minutes. Then add in the minced shallot and garlic and saute for 2-3 minutes or until they begin to soften. You aren't cooking the shallot and garlic to completion - only getting them started.
If the pot has any brown spots from the saute process then deglaze with a little bit of the broth, stirring the bottom of the pan with a wooden spoon with pressure until the brown spots are gone. Brown spots might cause the Instant Pot to not come to pressure.
Add in the rinsed and drained rice, vegetable broth, capers, lemon juice and zest, thyme, tarragon, salt, and pepper. Top with the sliced lemons and fresh thyme sprigs.
Close the lid and vent. Manually set the timer for 22 minutes at high pressure. It will take about 10 minutes to come to pressure.
After the timer has counted down to zero, do a 5-minute natural release. Then carefully do a quick release. When the pressure has been fully released and the pin is down, carefully open the lid.
Remove the lemon slices and sprigs of fresh thyme. Fluff with a fork and serve.