Yes, an LTE UE can have multiple IPs.
The UE can access multiple PGW/APNs in the same EPC core network and the UE will be allocated one IP per APN at the time of attach itself.
-> UE will be allowed to create one default bearer per PGW/APN.
-> For example in the case of VoLTE User there can be at least two APNs (two IPs), one for normal internet access and the other one for IMS access.
