From what I know (which ain't a lot of the history), the earliest lx200's had round DIN connectors and ran on 12 volts DC. At some point they changed to the modular plugs that we see now (think phone and network type wired connectors) and changed to 18 volts DC. Later they changed back to 12 but I think those are not classics.
In any case it's the models that say 18VDC by the power connector that you have to be concerned about the capacitors mostly. What happens is that the Meade power supplies are not well regulated and can send the voltage spiking higher than the caps are rated for. When a cap gets over-voltage it blows up. The problem is that the early tantalum caps that were used when these were built tended to blowup like a small incendiary bomb and burn anything nearby. Don't be too alarmed by that description. Think the size of the cap guns we played with in the 60's, not a firecracker or larger. It will take out something close but would be very unlikely to get outside the case. Newer tantalum caps don't do this as often so they are safer. And most people replace then with electrolytic's which only smoke and stink.
Something else to keep in mind... Any components can just decide to quit working at any time, so don't always blame the power supply if it quits.
If it's been sitting in a box for years the electronics should behave, at least for initial testing. I would be more concerned with the mechanicals. Think grease, dust, rust, corrosion, fogging of the glass/mirrors.
What I would do is a very complete visual inspection inside and out. Not taking apart the scope itself but the drive assembly. Take the covers off of the bottom and sides and look closely. Then if you have 1, put a volt meter on the power supply before you connect it to the scope to check that it's putting out close to the right voltage. If I remember the caps are rated at 24 or 30 volts so anything near 24 or higher may next looking at. If everything looks good then pray and plug it in. Before you turn it on check the base and power supply (PS for short) for heat. The PS will be warm just being plugged in to AC but not HOT. Then turn it on and again check for heat, smoke, unusual noise. They do make some noise at startup but not a lot. Also look at the AMP meter on the base, if it stays with all bars lit up there's probably something sticking and drawing excess power.
If it passes all this put it through it's paces and see how it does.
Let us know how it goes.