Lexical rules are a type of deterministic grammar rule, and internal rules are a type of probabilistic grammar rule. and below are examples of lexical rules and internal rules for the sentence “Workers dumped sacks into a bin.”

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Standard lexicalized grammar is a type of grammar rule where each non-terminal node in a  lexicalized parse tree is associated with a lexical head (the headword) and a head tag, and the head tag is the part-of-speech tag of grammar. Below is an example of a parse tree for the sentence "Workers dumped sacks into a bin.".

Standard Lexicalized Grammar 

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Lexical Rules and Internal Rules

The Collins parser divides a constituent into a non-terminal head, non-terminals that are on the left of the head, and non-terminals that are on the right of the head. Abstractly speaking, $$LHS=L_n L_{n-1}...L_1 H R_1 ...R_{n-1}R_n$$, where $$L_i$$, $$H$$, and $$R_i$$ are symbols representing its category, head, and head tag, such as VP(dumped, VP) in the example sentence “Workers dumped sacks into a bin.”

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