I don't know if it is the same for cities in Rheinland-Pfalz but I believe Berlin abandoned Local Mean Time in 1893 in favor of CET (Central European Time UTC +1). Currently Rheinland-Pfalz uses CET in winter and CEST (Central European Summer Time UTC +2) in summer.

LMT Local mean time differs from apparent solar time as can be observed with a sundial in that time is constant with LMT but the speed of time varies with a sundial.

This is all confusing without examples so...

At Mainz on this year's summer solstice, the sun will rise at 5:17 CEST, reach solar noon at 13:28, and set at 21:39 CEST.

And on this year's winter solstice, the sun will rise at 8:22 CET, reach solar noon at 12:25, and set at 16:27 CET.

There are (by subtraction) 8 hours ten minutes between noon and sunset midsummer and 4 hours between noon and sunset midwinter. This explains the timing of the candle law.

Edit: But it's also important to recall that sunset isn't the time it gets too dark. There are 3 phases of twilight. During Civil Twilight it is generally possible to do outdoor activities though the sun is below the horizon. During nautical twilight, if the sky is clear, the brighter stars are visible and so is the horizon. During astronomical twilight, some stars that would otherwise be visible are obscured by sunlight.