Heat oil on the saute setting of a 6-quart electric pressure cooker. Cook ham strips for 6 to 8 minutes, stirring, until their edges brown and the meat reaches 165°F; transfer to a plate.
Add fennel and shallots to the cooker and cook for 5 minutes. Stir in garlic for 30 seconds, then pour in 1 cup of the broth and scrape the bottom completely clean.
Add navy beans, remaining broth, thyme and pepper. Check that the contents stay below the cooker half-full line for beans, lock the lid and cook on high pressure for 35 minutes.
Allow pressure to release naturally until the indicator drops, about 20 to 30 minutes. Open the lid and check that beans are completely soft; if still firm, pressure-cook for another 5 minutes and allow a natural release again.
Discard thyme stems and blend carefully with an immersion blender until smooth, keeping the blade submerged. Stir in lemon juice and add up to the measured hot water if the puree is too thick to pour.
Taste before adding up to the measured salt. Rewarm ham strips over medium heat in a separate small skillet to 165°F if needed, then divide soup among six bowls and add the ham on top.