The phrases conjoined by "and" have to all be of the same grammatical type, and the new phrase created will also be of that same type. That's the only principle involved here, though the details are complicated. In the example, there are 3 phrases conjoined, so all three should be the same type, but they're not:
... by [evaluating customer needs], [identifying], and [implementing a solution]
We have three gerund forms of: (a) a transitive verb phrase ("evaluate customer needs", (b) a transitive verb ("identify") without a direct object, (c) another transitive verb phrase ("implement a solution"). So that's the problem here. A verb has been conjoined with verb phrases, and a verb is not the same type as a verb phrase, since verb phrases include direct objects.
The most straightforward way to fix this is to supply a direct object for the verb "identifying" --
... by [evaluating customer needs], [identifying a solution], and [implementing the solution]
-- because now, we'll have three verb phrases, all the same type, conjoined by "and". This is grammatical, unlike the first version. However, it has become a little wordy. A more involved way to fix it is the one you've suggested, which has two "and" conjunctions, one inside the other:
... by [evaluating customer needs] and [ [[identifying] and [implementing]] a solution] ]
The first "and" connects the two verb phrases (a) "evaluating customer needs" and (b) "identifying and implementing a solution", where the (b) verb phrase consists of a verb "identifying and implementing" and a direct object "a solution". "Identifying" is a transitive verb, "implementing" is a transitive verb, so when they are conjoined by "and", we get a phrase of the same type: a transitive verb "identifying and implementing". This transitive verb, then, combines with "a solution" to form a verb phrase.