Air carrier Captain reported an ATC failure to separate aircraft resulted in a NMAC. Captain also reported uncertainty of airport and ATC service limitations from ATIS and NOTAM.

Narrative

We were descending into Lagos Nigeria expecting vectors for the ILS 18R. ATIS reported 10 km visibility with a scattered layer at 1;400 ft. and landing Runway 18R and Runway 18L. There was no mention of what type of approaches were in use. The initial Approach Controller told us to expect ILS 18R. When we were handed over to the final Approach Controller; we were told to fly direct to the LOS VOR. This is not normal but it seemed ATC was task saturated. I assumed this was for spacing. I thought we would be cleared for the ILS at some point prior to the VOR. ATC was keeping us high at FL50. We asked for lower. ATC told us to maintain FL50 and to report overhead LOS VOR. At this point we assumed we were going to be flown over the airport and then vectored downwind. When we reported over the VOR; we were told to report when we were outbound. It kind of looked like we had just been vectored for the full VOR ILS 18R approach without being told. I also concluded that this was happening because ATC traffic radar must have stopped working. We quickly established ourselves outbound on the VOR holding pattern and reported that we were outbound. ATC then told us to descent to 2;500 ft. Unfortunately; there was an airplane directly in front of us. The airplane was 500 ft. below us; crossing right to left and climbing into our approach path. We told ATC we were unable to accept the clearance do to traffic in front of us. ATC then aggressively told us again to descend to 2;500 ft. Right after that call; we got a TCAS traffic advisory on the airplane ahead of us. At no point did we receive an RA advisory. I deviated slightly right of course to ensure we would pass behind the conflicting airplane with adequate spacing. We waited until we were clear of the potential conflict and then started our descent to 2;500 ft. I can only assume ATC wasn't aware of the location of the traffic in front of us. This is most likely because the ATC radar was not working. ATC then told us to turn inbound and report inbound. After we reported inbound we were cleared for the ILS straight in approach. ATIS did not report what approaches were in use. ATIS did not report ATC radar as being out of service.ATIS did report VMC conditions. There were no NOTAMS for an inoperative radar at the LOS airport. We made several radio calls to ATC for clarification of what we were doing. As I mentioned earlier; they were completely task saturated and as a result we were unable to get a clear picture of what ATC's intentions were for us. So we were never cleared for the VOR ILS 18R approach. We were basically told to fly the procedure and when we turned around flying back towards the airport; we were then cleared for the ILS 18R approach. The ILS 18R approach is the approach we briefed. We can't say we were flying an approach we didn't brief because we were never cleared for the VOR ILS approach. We basically flew the procedure in VMC conditions. ATC was clearly using the full VOR ILS approach to sequence aircraft in a non radar environment without protecting the airspace on the holding side of the procedure turn.