The best reference I could find is from British Library Sounds web page:
lle chwech≠9 (source of well-known Welsh joke that toilets are more expensive in Wales than in England as “chwech” also used for ‘six’≠, i.e. five pence more than “spend a penny”, possibly thought to derive from “rhech” Welsh for ‘to fart’≠)
≠see Geiriadur Prifysgol Cymru (online)
9See also Robert Penhallurick’s The Anglo-Welsh Dialects of North Wales (1991, p.226) Cl1 Llanfair Talhaiarn.
Another possible explanation I've found is that lle chwech (which translates to "six place") refers to the workers toilets which commonly have six seats. I've found this explanation in three different sites (two of them are answers in a forum and one of them is a comment in a blog page). The people who provided the explanation appear to be of Welsh origin.
It's kind of our version of 'outhouse' - comes from workers' toilets, where you'd commonly have six seats in a row
Welsh: Y posibilrwydd arall (fase'n esbonio pam fod y term yn bodoli mewn rhai ardaloedd gogleddol yn unig) yw fod e'n dod o ardaloedd y chwareli a mwynau copr, lle roedd cwt 'ty bach' gyda lle i chwech person yn unig.
English translation: The other possibility (explaining why the term exists in some northern areas only) is that it comes from the areas of quarries and copper mines, where there was a 'small house'(toilet) cabin for just six people.
The Welsh euphemism for ‘toilet’ is a literal translation of “little house” (tŷ bach) the standard word you’d see for example on public signs would be “toiledau” (toilets).
There are other Welsh euphemisms for ‘toilet’ but the common North Wales dialect one is “lle chwech” which translates as “six place” usually explained as referring to workplace toilets where you’d commonly have six seats in a row?
Furthermore, I've found a supporting evidence for the second theory in an archaeology book written in Welsh. It provides a reference to a six-seater privy in a quarry in north Wales. Here is the excerpt and the image from the book Llechi Cymru: Archaeoleg a Hanes (by David Gwyn):
Anaml iawn y gwelwyd toiledau tan yr ugeinfed ganrif. Mewn rhai mannau, mae seddi dwbl o slabiau wedi goroesi dan ddaear, fel yn chwarel Cambrian yng Nglyn Ceiriog a oedd, fwy na thebyg, ar un adeg yn gysylltiedig â chlosedau pridd, er ym Maenofferen, defnyddiai'r dynion blanc dros sianel ddŵr a redai'n gyflym tan 1996. Yn chwarel Oakeley rhoddai rhes o gabanau heb ddrysau arnynt olygfa arbennig o dref Blaenau Ffestiniog. Mae magic flute chwe sedd wedi goroesi ym Mhen yr Orsedd. Cai hwnnw ei fflysio gan fwced y byddai dŵr yn cronni ynddi nes bod digon o bwysau ynddi i'w gwagio (Ffigur 163). Roedd closedau dŵr canolog ar gael yn y Penrhyn erbyn y 1950au.
English translation: Privies were few and far between until the twentieth century. In some places double-seater slab seats survive underground, such as at the Cambrian quarry in Glyn Ceiriog, which presumably at one time were associated with earth closets, though at Maenofferen the men used a plank over a fast-running water channel until 1996. At Oakeley quarry a row of door-less cabins commanded a magnificent view of the town of Blaenau Ffestiniog. A 'magic flute' six-seater survives at Pen yr Orsedd, flushed by a tipping bucket in which water accumulates until the weight empties it (Figure 163). Penrhyn had acquired centralised water closets by the 1950.
Ffigur 163. Lle chwech ym Mhen yr Orsedd, Nantlle, gyda dull fflysio awtomatig yn yblaendir.
English translation: Figure 163. Pen yr Orsedd privy, Nantlle, with automatic flushing mechanism in the foreground.