If two aircraft are on VOR radials that are apart by 15 degrees or more and one aircraft is at least 15 DME out, they are considered laterally separate. I read this rule in ICAO documents but my question is what if radials are 180 degrees apart and one aircraft is 15 DME out? Would they still be considered separate? I don't think so because they would be reciprocal to each other in this case. Then what are the limitations of above mentioned VOR separation rule?
The mentioned VOR separation does not apply that way.
If one aircraft is moving towards the VOR on radial 90 and other is also moving towards the VOR on radial 270, both are maintaining FL360 and first aircraft is 15 NM away from the VOR, are they separated?
Both aircraft in this scenario will be on a head-on collision course.
ICAO Doc 4444 references Annex 2 Appendix 3 for the table of cruising levels. In your scenario both aircraft should not be on the same FL, and should be separated vertically (the east/west or north/south rule depending on the country). (Does ATC direct flights to fly eastbound at odd levels and westbound at even ones?)
The reason for that criteria shown above is because of the 95% containment of the VOR when less than 50 NM away is 4 NM, that is the plane can be left/right of the radial by upwards of 4 NM. To understand that, move both planes closer, still on the same 15° separation, and take into account that they may not be exactly on the radials (loss of lateral separation).
The VOR separation you quoted takes that into account, but not to the full extent, for that reason some states say it should be increased to 30° (from 15°), or make it 35 NM at 15° (not 15 NM). (Twenty-Eighth Eastern Caribbean Working Group Meeting)