paddyjnr, your question is a little confusing, I am not exactly sure what you are asking. You make reference to Invalidity Pension but provide a link to Partial Capacity Benefit. You say you cannot get the household benefits because of a lodger? Is that correct?
I think what you are trying to say is that if you start back working over a certain threshold this will affect your invalidity entitlements? And that because you have a lodger you will not be able to avail of certain benefits?
Just to note, disability and invalidity are not actually comparable. Any distinction is not exactly unfair when you think about what the two words mean.
Broadly speaking, invalidity essentially is a case where you are currently unable to work because of an illness, however at some point in the future that may change. Invalidity pension would apply where you have been unwell for a prolonged period of time with little or no likelihood of that situation changing in the short term - based on the assessment of a medical professional. It gives you access to more and makes it less onerous for you to claim it (as gipimann pointed out). Invalidity, in other words, means there is the possibility you will "get better".
Disability on the other hand is a life-long condition of some description that is to your detriment in society. It may not prevent you working and participating fully in society but it will never go away and you probably have to make accommodations to it for example wheelchairs, guide dogs, hearing aids, supported living, specialised cars, etc. You will always live with your disability. There is (generally) no getting better.
That is a gross generalisation of course, there are people on invalidity who will never realistically be able to come off it. And there (hopefully) are people whose disability may be "corrected".