If I call my local representative on the phone, or email them, that's lobbying. Am I not allowed to contact those I've elected to represent me?
Now, if you mean I shouldn't be allowed to take my representative on a Caribbean vacation, then we're agreed, because bribery is (or should be) illegal. And yes, I'm including many forms of campaign donation as "bribery".
Depending on what you mean by local, you're never going to be able to directly contact your representative. Your phone call, if answered by a human will be an intern or other sort of assistant who will basically end up marking you as a tally on whatever side of an issue. You will have near zero influence. Emails are even worse. I'm sure now a days you'll get LLM slop but 'back in the day' you'd get a response that always came down to "Thanks for your message. Representative Joe Blow likes good things, and dislikes bad things. And he even thinks important things are important! Thanks for your message, and remember to vote for Joe Blow! Bye!" Even better, you get subbed to a bunch of donation begging mailing lists.
By contrast go buy a top dollar lobbyist, and he'll go endlessly push your issue to all his old buddies. He'll even compose legislation that can be rubber stamped by the reps that your lobbyist will know are most inclined to agree with. You'll get better than direct contact and over a sustained period of time if necessary. I don't think the two are in any way comparable.
I don't know why people read stuff like this and then put themselves in corporate's shoes who can lobby up to 100s of millions
when is the last time you lobbied 50 million dollars as a citizen? is this something you do frequently? maybe ask these questions before your gotchas