I agree that the situation is exactly the same as if you were living in Great Britain (i.e. in England, Scotland or Wales).
However since you're obviously not using Llloyds in Northern Ireland (because Lloyds doesn't operate there) you've still got the problem of making an inter-bank transfer. It used to be really simple (as you just needed to fill in a free 'bank giro credit' form) but banks now typically charge £30 for an inter-bank transfer, which you'd obviously be keen to avoid.
However the solution may well be to use your local Post Office branch. You can withdraw cash (free of charge) from accounts with most banks that operate in Northern Ireland (such as Bank of Ireland, Danske Bank and Ulster Bank) at any Post Office branch. You can also pay into a Llloyds account (free of charge) at any Post Office branch. So, by combining the two, you can transfer money from your Northern Ireland account into your Lloyds one.