The result of the distance() function is unused and can be optimized away by the compiler. Runs in 0.04s with LuaJIT 2.0. No type declarations needed. :-)

    local radius = 6371

    local function distance(latA, lngA, latB, lngB)
      local latAr = math.rad(latA)
      local lngAr = math.rad(lngA)
      local latBr = math.rad(latB)
      local lngBr = math.rad(lngB)

      local deltaLat = latBr - latAr
      local deltaLng = lngBr - lngAr

      return radius * 2 * math.asin(math.sqrt(
              math.sin(deltaLat/2)^2 + math.cos(latAr)
              * math.cos(latBr) * (math.sin(deltaLng/2)^2)))
    end

    local start = os.clock()

    for latA=-90,90,2.5 do
      for lngA=-90,90,2.5 do
        for latB=-90,90,2.5 do
          for lngB=-90,90,2.5 do
            distance(latA, lngA, latB, lngB)
          end
        end
      end
    end

    local stop = os.clock()
    print(stop-start)