Because English does not have a case system. In languages like Russian, German etc. words have different endings based on their position in a sentence. So, it's clear what you meant because lady would be in the objective case and dog in the nominative. In English, however, the word lady and the word dog will look the same no matter its place: our only cases are possessive and plural, and pronouns have distinctive subjective and objective cases, and nouns have plural forms (unlike in Japanese,) but these cases are not nearly as extreme as in other languages. This is why word order is very, very strict in English.

You could say 'The lady was bitten by the dog' which would make the sentence a passive sentence. Alternatively you could say 'The lady, who the dog bit...' or 'The lady, (who was) bitten by the dog'. In each of these sentences the 'lady' is mentioned before the 'dog' Where word order is concerned I do believe our structure is very lax compared to that of other languages such as German. We may have rules for 'Standard English' but these rules are rarely followed in spoken, or even in written, English.

Hi Vance I won't attempt to answer your first question about strictness of word order, but very often changing the word order also changes the meaning, so you have to be careful to say what you intend to say. In your example, you CAN say: 'The lady the dog bit', where the lady is the subject, but the meaning is different to 'the dog bit the lady', where the dog is the subject.