All EU/EEA lanes are set up to process travellers with any passport, as foreigners travelling with a British or other European spouse may use those lanes. However it seems that MAN is an anomaly when it comes to letting ILR holders use the EEA queue on their own.
Each time someone with ILR enters the UK, the immigration officer must reassess whether their ILR is still valid, i.e. that they are still resident in the UK. If the person indicates that (s)he is not resident in the UK and that their non-residence is not temporary and lasting less than 2 years, the ILR should be cancelled and the person either denied entry or given leave to remain as a visitor.
I expect the majority people with ILR will only hold it for 12 months before applying for British citizenship (which can take a few more months), so it isn't the end of the world. If you are at the front of the plane the non-EU queue may be faster anyway.
If you aren't a US citizen and not travelling with one, see what happens if you try to enter the US in the citizen's lines.