A little backstory;
In the fairly recent past, there were a spate of people posting that they were unable to send emails for no obvious reason, the email client would often just return a fairly generic 'password is wrong' message. Oddly enough (or so it appeared to them) they reported that they could send out using the VM webmail system, and it also works if they connect to a different wifi or use their phone's data connection.
What had happened is that a device on their home network (not necessarily their PC, in fact it generally wasn't) had picked up a bit of malware and was happily sending out spam. This had been reported to or picked up by Spamhaus who added their address to their blocklist - the SBL, or we might refer to it as the naughty list. Note that the company also maintains other lists of IP addresses (the PBL for example) that your address should be on and this doesn't cause any issue.
VM decided that they would check this list as part of the email sending process (a bit of a simplification but you get the idea), so you send a message, it hits VM's servers, they check the list, see your address is on it and reject it - email clients didn't understand this and just reported a generic error. It was all a bit sledgehammer to crack a nut but that's what they did. Naturally if you were on someone else's wifi then the address was different and chances are it would work. VM's webmail used a different method and wasn't affected by this.
The problem was that the offending device sending out spam could literally be anything you had connected to your home network (Amazon Firesticks with some dodgy third-party software seemed to be a regular culprit) - and tracking it down could be a bit of a faff. There was no point in just trying to get your IP address changed or requesting a delisting without finding the reason for being listed. Otherwise in very short order, you'd find yourself listed again!
Now the reason for the long (and probably boring and irrelevant) explanation is that it appears that VM are running their own in house blacklist, but at least this time you get some kind of meaningful message returned. What we don't know is how VM compile the list - is it just a downloaded copy of Spamhaus' list or someone else's or something they've cooked up themselves?
In any case at least you know who to contact to request a delisting (although how exactly do you contact the abusedesk? By email - I can see a problem with that!); although if you were to call the normal customer services number and the offshore helpdesk staff even understand what you are talking about, I'd be astonished!
All that aside; it's one thing to get delisted and another to stay off the list. Unless you have been unfortunate to be hit by a false positive (which is not impossible); then without discovering and eliminating the reason you are on it in the first place, your ability to send mail is likely to be short-lived.
As an experiment, can you see if you can successfully send a message via the webmail interface?
@ModTeam look I do appreciate that this is just screaming into the void but to back up @ravenstar68 is there any way of getting the CS team to stop just making stuff up if they don't know just to be able to close a call? Unless, of course their scripts really do say that the IP addresses regularly change - in which case the training and thoroughness is even worse than we assume it to be!
Don't tell me that LG have contracted the lowest possible bidder to run their helpdesk - I'm shocked!