I've seen people run LPS/SOX lamps on fluorescent gear, typically instant-start electronic fluorescent ballasts. Is that bad for the lamp? I know that the OCV for LPS is around 600v, but the high frequency?

Not sure about what a T8 ballast gives out, but I believe SOX runs quite well on high frequency square wave supplies.

 Any two lamp F32 instant start ballast with it  output combine
  Will drive a  35/ 55 watt Sox and  58 watt fluorescent as well
  On instant start.   And make sure is has ballast factor of 1 or better.   Below that is usually the crappy residental grade ballast
  That under drives the F32.

Make sure is has ballast factor of 1 or better.

Isn't a power factor of 1 as good as it gets?

I wonder why high frequency electronic ballasts cannot be used to operate HID lamps, but can be used on t8 fluorescent lamps and LPS lamps. Is it because of the amount of pressure in the arc tube?

The arctube is a hard thing, filled with anelastic material, aka the gas. It forms an accoustic resonator, with a rather high quality factor (mainly when thick and not that long). So it does not tal much energy to excite there standing wave there, with rather high peak pressures. This as first is loading the arctube by just that peak pressure the arctube has to hold and as second influences the arc parameters (high pressure means higher voltage drop, so higher power density at that spot). If the drive frequency matches the tube resonance, it may excite rather high amplitude waves

Low pressure lamps are rather large, so the resonant frequencies are low and  the large surface to dissipate the vibrations means rather low Q, so even if you match the resonance, the amplitude is not that big. Plus low pressure devices are in fact vacuum operated devices, so even when the standing wave amplitude is relatively large (vs the fill pressure; the sound pressure amplitude can not go above the absolute static pressure), in absolute numbers it is still very low (we are talking about few Pascals here).
Plus tge thermal loading is very low, so even when the thermal nonuniformities from standing waves appear, usually the material has margin to handle it.
So although 50Hz may be close to that resonance, it does not do much. And the 20+kHz is so far above the resonance, it does not excite anything.

But in high pressure lamps, when the fill pressure is e.g. 10 bar when burning, the standing wave could reach another 10 bar, so the arctube has to suddenly handle 20 bar pressure instead of 10 and that is a huge difference. Plus the small size makes the accoustic power dissipation rather low, so yields very high Q resonator, so once you match the frequency, it can boost the pressure a lot with not much stimulation.
The 50Hz is way below the resonance, so it does not excite anything, but the 20..100kHz is where significant resonance peaks are, so not that difficult to excite. The thing is, the resonance frequency depends on what happens in the arctube, so whatever frequency you choose, the arctube tends to "lock in" on it, so even whenthe high Q means rather narrow frequency peaks so low chance to hit it, the lock-in mechanism makes practically sure the resonance gets excited.

I know many did experiments with modulating the ballast frequency, so its spectru  is spread, with rather low energy fitting into thd resonance bandwidth, but that made the lamp power modulated along with that, reducing the lamp efficiency. With the complexity it made these ballasts not a viable way, in contrast to not that mych more complicated LFAC ballasts feeding the lamp with a rectangular wave and sticking at the ideal operating point.

Only some HPS high frequency ballasts made it till production, as HPS are technically rather a medium and not high pressure lamps (working pressure is around atmospheric), plus using rather thin arctubes, which made them more robust against the resonance effects (thin tube means large viscosity losses for any vibration waves lowering the Q plus easy to handle the extra pressure, plus not that high pressure to start with).

I wonder why high frequency electronic ballasts cannot be used to operate HID lamps, but can be used on t8 fluorescent lamps and LPS lamps. Is it because of the amount of pressure in the arc tube?

There are electronic ballasts for HID lamps, look at the Philips CosmoWhites, for example. Don't know what the frequency of the output is, though, I've never bothered measuring it. You've got me intrigued now, will have to fetch one out and get it on the 'scope.

I think instant-start electronic fluorescent ballasts operate at 30khz because they make a high-pitch sound when powered on.

Electronics for HID lamps are outputting a squarewave AC current at about 150-300 Hz. This was optimized for minimal flicker while still being far from acoustic resonance and probably for less lamp buzz. Of course, that requirement makes HID electronic ballasts over-complicated, compared to fluorescent lamps which are happy at 30 kHz sinewave.
 

will have to fetch one out and get it on the 'scope.

Be careful until you are fully understand what are you doing and the schematics. Both lamp ends are floating from the the ground and there are ignition pulses capable of killing scope input even with 1:10 probe!

From my experience, I have used magnetic pulse start metal halide ballasts to run SOX low pressure sodium lamps with the original ignitor replaced with a dedicated SOX low pressure sodium ignitor and the lamps ran very well.

For example, I have used a 70w M98 pulse start metal halide ballast in conjunction with a Philips SX76 ignitor imported from the UK to run a 90w SOX low pressure sodium lamp, and the lamp ran at its specified arc voltage drop and operating current.

https://www.lighting-gallery.net/gallery/displayimage.php?album=search&cat=0&pos=6&pid=210357

What is the typical OCV of an LPS/SOX lamp? Do some run at 600v and some run at 50v?

The striking voltage of most lamps 35W and upwards is typically 500-600V, although 10W and sometimes 18W lamps can strike on 240V mains a lot of the time.

It is also good to note that SOX low pressure sodium lamps between 18w and 90w can be operated on 220v-240v series choke ballasts in conjunction with a special ignitor such as the Philips SX76. However, you will need a very high OCV HX autotransformer ballast to get the 135w and 180w SOX low pressure sodium lamps to start and run, but sometimes, there are 135w and 180w SOX low pressure sodium HX autotransformer ballasts that use a special ignitor as well but have a lower OCV than typical 135w and 180w SOX low pressure sodium HX autotransformer ballasts.

I've lit MV and HPS on fulham WH ballasts, though the ones I've used wouldn't supply enough current to run them to full tilt. I have had great success so far with the WH3 running SOX 18 & 35 so far in the same config, in fact that's all that I have been using on my SOX lamps since US spec magnetic ballasts are expensive hens teeth.