The lam at the beginning of words is of two types: the lam that accepts the sukun and is clearly read and the lam that does not accept the sukun and is not read but simply written.
Does this rule apply to reading in Arabic in general or only to reading the Qur'an?
Yes, it applies to both Modern Standard Arabic pronunciation and the Qur'an reading. It has to do with the so called 'moon' and 'sun' consonants. The 'sun' consonants are sibilants and dentals. The 'moon' consonats is everything else. The [l] of the definite article 'al- is assimilated to the 'sun' consonants and not assimilated and hence pronounced with the 'noon' consonants. It's true also for spoken varieties of Arabic.
This is a description of the assimilation of laam to the following “sun letter”. It is a description purely in terms of Arabic orthography, not of scientific phonology and phonotactics. In the word الشمس “the sun”, the laam has no diacritic and is not pronounced as /l/, while the following shiin is written (in vocalised script) with tashdiid, indicating that it is geminated. The word is thus pronounced as ash-shams.
The gemination of the “sun letters” is a feature in all stages of written Arabic, and also of the modern dialects, but it does not have a totally predictable phonological rationale. For example, in most dialects the historic jiim is a dental /dƷ/, but is nonetheless treated as a “moon” letter, while in Egypt it is /g/, but it is a “sun” letter. This has a historic reason.
