No, you can't tell by the colour of the case.
As the extract of the schematic shows, this unit uses a PIC instead of a pair of ADD3701 DVM chip. This means it comes with the later innards.
The change was prompted by the ADD3701 going EOL, and it happened before the cases changed colour.
The way to tell at a glance is to look at the damping switch. On the later models, it's a small square push-button. The earlier "bird's nest" models used a larger rocker switch.
That is a much neater an more modular layout, and I see that the display as well as the pots are mounted differently. Mine is an older version with point to point wiring and the ADD3701 rather than a PIC. The two examples I have here do have different damping switches, but both are rocker types. I have added a couple of pictures whuch might help to identify the specific board.
Good to clarify that, as your original post pointed very definitely to the Mk2, given the schematic extract from the later models. As I say, the colour of the case is meaningless with these - the damping switch (and position of the earth binding post) is the way to tell them apart from the outside.
In the earlier units, there's no driver chips - the display is driven directly from the ADD3701, which includes LED drivers as part of its design (just needs cathode drivers, which is simply 4 transistors in the PL320 design). Just in case you haven't already seen it, the manual for the earlier models is here:
https://web.archive.org/web/20140408222743/http://k1.dyndns.org/Vintage/Sinclair/Other%20Inventions/Other%20Electronics%20Products/SINCLAIR%20THURLBY%20PL%20SERIES%20POWER%20SUPPLY.pdfAnd if anyone needs the later one:
http://www.chriswilson.tv/PL_Series.pdfAnd the ADD3701 datasheet:
http://pdf.datasheetcatalog.com/datasheets/560/502474_DS.pdfNo idea if it's possible to find the original display type new today - you might be lucky and find a NOS item, or perhaps someone has a spare from a donor item - they were widely used back in the day, so the odds are good. Thurlby used them in their logic analysers and some of their bench multimeters, for example. But modern 4-digit common-cathode displays are widely available - the challenge being getting the right physical dimensions to fit the opening in the front panel. Wiring them up is the easy part, though might not be pretty - but least that's in keeping with the rest of the instrument

Another thing to check with a "drifty" Mk1 - the presets can get iffy with age. Unfortunately, most of them have far too much range, so the setting of them is very difficult to get right. PR1 is worth checking if the output voltage is genuinely drifting (deciding if it's the PSU or the meter is obviously the first step). If you're feeling keen, it's worth changing resistors either side of the pre-sets to give the pre-sets much less range. The trouble with this design is the pre-set has to include enough range to cover the tolerances of the tracks in the voltage pots, which could easily be +/-20% (though the NOS Colvern WW pot I've got standing by actually measures within 2% of 50k, which is pretty respectable). Even so, there's still far too much range. The Mk2 removes the pots from the feedback network, replacing them with a fixed resistor - this means the pots can be cheap and nasty consumer-grade types, and the "set max" pre-set can have less range, leading to better "setability" and stability.
These earlier units might be a bit ugly internally, but they are generally very reliable once restored, and are well-worth the effort. I've worked on far worse.
Oh, you mentioned units with LCD displays - presumably these were a TS series? The ones I've seen use ICL7106-like display chips, that are 2000-count units. That means that they auto-range to 100mV resolution as they get close to 20V. I can't remember what the current meter does - it either has 1mA resolution, but can't read over 1.999A, or it has 10mA resolution (think it's the former, but would have to dig mine out of storage to check). Only the 4 amp TS units came with an auto-ranging current meter. The PL series maintains the 10mV/1mA resolution across the whole range, which was unheard of at that price point when they were introduced, and is still very respectable today. I think the TS series was a "cost-reduced" version of the PL models - I don't think the dual models came with the series/parallel/tracking modes that the PL QMD have (mine doesn't, at least). Nice enough, if the metering is good enough for your needs - the build is not all that dissimilar to the later PL models, with sensible modularity, etc.