I am sorry to be the bearer of bad news, but the short answer is yes, Lowells do have the right to register this against your credit file because as far as they are concerned, the dispute was not decided in your favour by the Ombudsman.
I would suggest that you ask the Ombudsman to provide a letter stating that the mount is in dispute and is being investigated. You should be able to send this to the credit reference agency and request that they place a note on your file or remove the record.
As it stands, the entry which appears on your credit file seems to be correct, based on the information you have provided above.
I would also suggest that you contact the credit reference agency and raise a dispute with them.
I hope this answers your question. If so, kindly rate the answer and provide feedback.
If you have any further questions, please do not hesitate to ask.