In the US, the Lara with a C pronunciation is unusual and sounds a bit pretentious, unless you've got a European accent of some kind.
This is making me think that I misunderstood how the OP is pronouncing
Lara. I pronounce
Lara so that the A in the first syllable is the same as the A in "cat." So I pronounce
Clara like
Lara that way with a C in the front, and that's the only way I've ever heard any American pronounce it. If
Lara instead is pronounced so that the first syllable rhymes with "car", and thus
Clara is also pronounced with the first syllable rhyming with "car", then I agree with you.