Our previous identification and spectroscopic confirmation of 431 faint, new planetary nebulae (PNe) in the central 25 deg2 region of the Large Magellanic Cloud (LMC) permit us to now examine the shape of the LMC planetary nebula luminosity function (PNLF) through an unprecedented 10 mag range. The majority of our newly discovered and previously known PNe were observed using the 2dF, multi-object fibre spectroscopy system on the 3.9-m Anglo-Australian Telescope and the FLAMES multi-object spectrograph on the 8-m Very Large Telescope. We present reliable [O iii] 5007 Å and Hβ flux estimates based on calibrations to well-established PN fluxes from previous surveys and spectroscopic standard stars. The bright cut-off (M*) of the PNLF is found by fitting a cumulative function to the bright end of the PNLF over a 3.4 mag range. This cut-off is used to estimate a new distance modulus of 18.46 to the LMC, in close agreement with previous PNLF studies and the best estimates by other indicators. The bright-end cut-off is robust to small samples of bright PNe since significantly increased PN samples do not change this fiducial. We then fit a truncated exponential curve directly to the bright end of the function over a 6 mag range and test the curve's ability to indicate the position of M*. Because of the significant increase in the number of LMC PNe, the shape of the PNLF is now examined in greater detail than has previously been possible. Newly discovered features include a small increase in the number of PNe over the brightest 4 mag followed by a steep rise over 2 mag, a peak at 6 mag below the bright cut-off and an almost linear drop-off to the faint end. Dips at the bright end of the PNLF are examined in relation to the overall shape of the PNLF and the exponential increase in the number of PNe. Through cumulative functions, the new LMC PNLF is compared to those from the Small Magellanic Cloud and a new deep local Galactic sample revealing the effects of incompleteness. The new [O iii] 5007 Å LMC PNLF is then compared to our new Hβ LMC PNLF using calibrated and measured fluxes for the same objects, revealing the effects of metallicity on the [O iii] 5007 Å line.