I agree there is no grace period for L-1/2. But I don't think USCIS will aprove c/s from L-2 to F-1 simply because the L-2 is not in lawful status when the school starts in June 20. L-2 was in status when the c/s was filed. That's not enough. USCIS will likely issue a RFE and hopefully the L-1 extension is approved at that time, provided L-1 holder has concurrently filed I-539 to extend L-2 status.
