Heat a medium saucepan over medium heat. Add bacon, and cook, stirring often, until crisp, 3 to 5 minutes. Transfer the bacon with a slotted spoon to a paper towel-lined plate to drain.
Add oil, onion, garlic, thyme, salt and pepper to the pot and stir to combine. Cover and cook, stirring occasionally, until the onion begins to brown and soften, about 3 minutes. Sprinkle flour over the onion mixture and stir to coat. Add broth and milk and bring to a simmer, whisking constantly. Add corn and potatoes, increase heat to medium-high and return to a simmer. Reduce heat to maintain a simmer and cook, stirring often, until the potatoes are tender, 4 to 5 minutes.
Transfer 1 cup of the soup to a blender and puree until smooth. (Use caution when pureeing hot liquids; see Tip.) Return the pureed soup to the saucepan along with chives, lemon juice (or vinegar) and the cooked bacon.
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