3GPP Release 15, the first 5G standard, includes protection of user identity privacy against IMSI catchers. These protection mechanisms are based on public key encryption. Despite this protection, IMSI catching is still possible in LTE networks which opens the possibility of a downgrade attack on user identity privacy, where a fake LTE base station obtains the identity of a 5G user equipment. We propose (i) to use an existing pseudonym-based solution to protect user identity privacy of 5G user equipment against IMSI catchers in LTE and (ii) to include a mechanism for updating LTE pseudonyms in the public key encryption based 5G identity privacy procedure. The latter helps to recover from a loss of synchronization of LTE pseudonyms. Using this mechanism, pseudonyms in the user equipment and home network are automatically synchronized when the user equipment connects to 5G. Our mechanisms utilize existing LTE and 3GPP Release 15 messages and require modifications only in the user equipment and home network in order to provide identity privacy. Additionally, lawful interception requires minor patching in the serving network.