So long as they are only a lodger and you provide at least 4 weeks notice in writing, then yes, the notice will be valid. The notice for a lodger is different from a tenant, if they are legally considered a tenant, this notice would not be valid, however if they are a lodger as you have suggested then yes. If they refuse to leave, you would require to take court action to remove them.
I shall provide you with a helpful link that will assist you in finding a solicitor/representative near your local area. This will provide you with someone nearby your area who can assist you if required.
I hope this information proved helpful. You will find a local solicitor who deals with these matters on the law society webpage which is as follows;
https://www.lawsoc-ni.org/solicitors (N. Ireland)
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