You are given an array of strings where each string contains alphabetic characters and may also include digits. Your task is to sort the array based on the following rules:
For each string, compute the sum of all its digit characters (0-9). If a string does not contain any digits, its sum is considered to be 0.
Sort the strings in ascending order based on the computed digit sum.
If two strings have the same digit sum, sort them lexicographically (dictionary order).
Example:
Input: ["abc123", "a1b2", "xyz", "45x6", "abc"]
After sorting first by digit sum and then lexicographically when necessary, the output should be:
Output: ["abc", "xyz", "a1b2", "abc123", "45x6"]
Implement a function with the following signature in your preferred language:
function customAlphanumericSort(array: string[]): string[]
Your implementation should handle the sorting as described. Consider edge cases such as empty strings or strings containing no digits. Please do not provide hints or explanations in your submission; just focus on the code implementation.