The Dunlops on my LML suggest 35psi front and back.
Don't be confused with what's on the sidewall of the tyre - that's not the recommended pressure for your machine, it's the maximum presuure recommended for the tyres.. If you run them at too high a pressure, you will have excessive wear in the centre, among other things...
Cap'n, I would suggest for your LML about 1.4 bar front (20 psi), 1.9 bar rear (27 - 28 psi). It would be slightly less for vintage large frame Vespas, which weigh less than the PX and LML, so Soyachips' VBB should be about the same as my Super on 1.3 bar front (18 - 19psi) and around 1.6 - 1.7 on the rear (23 - 25 psi). But do experiment and see what feels best.
(Handy conversion tool here: http://www.asknumbers.com/PressureConversion.aspx )
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