A320 Captain reported cabin pressurization and cabin lighting malfunctions during cruise flight. The pressurization problem resolved and the flight continued to the destination.

Narrative

When reaching FL350; received an ECAM 'CAB PRESS (Cabin Pressure) SYS 2 FAULT'. After performing the non normal procedures; I contacted Maintenance via SATCOM. Failure continued; and was written in the logbook. This airplane had this same issue a day or 2 before. about 30' after; still at FL350; Received an ECAM WARNING- EXCESSIVE CABIN ALTITUDE. Both pilots had immediately the O2 Masks on; I was PF; and continued to be PF; [requested priority handling] with ZZZ Center; Told them we were depressurizing; and descending to 10;000'. With the airplane and the situation under control; and about 1 minute into the descend; the ECAM Warning disappeared; and the lower ECAM was showing again the CAB PRESS page; SYS 1 working; and amber XX for SYS 2. Cabin Pressure was regained and I requested to stop the descend at FL250. We don't recall how high the cabin pressure went; but the O2 masks for the cabin were not deployed. Note; that a few seconds into the situation; the number 1 FA (Flight Attendant); Person A; called us; to inform about some anomaly with lights in the cabin. We told him to standby; and give us some time to talk to him. At FL 250; after checking everything; and considering back to a normal condition; and being about half way between ZZZ and ZZZ1; I took my O2 mask off; and requested the FO to stay with the mask on some more time.; I cancelled the [priority handling] with ZZZ Center; and requested to climb to FL 330 to have enough fuel to continue to ZZZ1. I called the number 1 FA; to retrieve his info. They had 2 chimes; all cabin lights went bright; then 2 more chimes; then; all Lights flickering for a while; then stayed bright. The FA lost control of the lights on the FA panel. Flight landed in ZZZ1 safely with no more issues.