** Australian mining stocks .AXMM advance as much as 2.5% to hit a lifetime high, while the broader benchmark .AXJO rises 0.8%

** Sub-index has gained 2.9% so far this week, set for their third consecutive weekly gain

** Copper prices rise to an all-time peak following the U.S. Federal Reserve's interest rate cut MET/L

** BHP BHP.AX, Rio Tinto RIO.AX and Fortescue FMG.AX gain 2%, 1.4% and 2%, respectively

** Rio hits a record high, while BHP touches a two-month peak

** YTD, AXMM up 37.6%, including the day's moves, outperforming a 6.2% gain on AXJO

(Reporting by Nikita Maria Jino in Bengaluru)

((Nikita.Jino@thomsonreuters.com;))