Yes this is correct. Those who have completed and passed the LPC have an exemption for SQE1 but have to complete SQE2.
This could be part of the reason why Reed Smith are not able to consider LPC candidates though, because the way they have designed their programme means you might not fit into the training structure they have designed due to these exemptions (that is a major assumption by me though).
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Interesting. I'm on the LPC right now and have managed to get through at least one of their stages after the automatic situational judgment test and it hasn't so far seemed to be an issue - although I'm not confident that I'll reach the AC itself.