There are mainly two kinds of DRX in LTE that are used to save UE power consumption. Specially in the idle mode, when UE wakes up from its sleep mode at the pre-defined paging frame and paging occasion. It reads PDCCH for paging RNTI (P-RNTI). If P-RNTI is being broadcasted then UE reads paging message to find its paging identity in the RRC paging message.
In short, when UE will be in DRX mode (sleep mode) it would not be able to read PDCCH. It reads PDCCH only when it wakes up. Once it wakes up from the sleep mode, it reads PDCCH because it wakes up only when it suppose to read paging frame and paging occasion.