Trim stalks from fennel; remove tough outer leaves from bulb. Reserve bulb. Bring fennel stalks, water, potatoes, red pepper, 1/2 cup of the vinegar, and 2 tablespoons of the salt to a boil in a large stockpot over high. Reduce heat to medium-high, and simmer 12 minutes. Add corn, and simmer until potatoes are tender, 10 to 12 minutes. Remove corn and potatoes; let cool.
Return fennel mixture to a boil over high. Add lobster; boil 10 minutes. Transfer lobster to a large bowl of ice water to stop the cooking process.
Cut fennel bulb crosswise into very thin slices. (Use a mandoline if you have one.) Cut corn kernels from cobs; discard cobs. If using large red potatoes, cut potatoes into eighths. (Leave small red potatoes whole.) Stir together sour cream, mayonnaise, dill, parsley, black pepper, hot sauce, remaining 3 tablespoons vinegar, and remaining 3/4 teaspoon salt in a large bowl. Add fennel bulb slices, potatoes, and corn; toss to coat.
Cut shell of lobster tail segments lengthwise on top and underside, using kitchen shears. Pry open tail segments; remove meat. Discard shells.
Melt butter in a large saucepan over medium. Gently add lobster meat; heat until warmed through, 2 to 3 minutes. Remove lobster, and cut each tail into 3 medallions. Serve with potato salad and lemon wedges.