Anyone who is in the Work Related Activity Group (WRAG) and has been on contribution-based ESA for 365 days anytime from 30th April onwards will have an opportunity for transfer to means-tested ESA (if they are eligible), otherwise their benefit stops. Yet another rubbish outcome from the Welfare Reform Act.
If you are in the Support Group (SG) no such time limit applies.
If your condition has got significantly worse since you made your claim, it is possible to ask for them to consider a change of circumstances and see if you can be assessed to go into the Support Group now (which requires higher levels of functional disability). You will need supporting medical evidence.
To check whether you could score enough points to go into the SG, look at direct.gov.uk/prod_consum_d...
Points for WRAG are on pages 17-23, and points for SG are pages 24-26. You can only count any mental health descriptors if you have been diagnosed with a MH condition such as depression and are being treated for it.
You do need to understand that they are quite tough about where they score you, so they won't apply if you just occasionally have a problem - but they are supposed to score what you can achieve reliably, repeatedly, safely and in a timely fashion - if you can't do something 51% of the time, it should apply. Lupus fatigue is hard to pin down, but it often means you can score because you either might not be able to do something in the first place, or it would cause such a serious after-effect that you couldn't repeat it or do anything else for the entire day.
An alternative method is to show you come under the Exceptional Circumstances Rule (ESA Regulation 35), which means you should get medical evidence to support a statement that there would be a substantial risk to your physical or mental health if you were found to be fit for WRAG.
Actually you need to ensure you can get supportive medical evidence right from the start - it is very helpful as long as it is specific, and not just a general confirmation that you have Lupus.
Once the DWP has decided which group you belong in, you have a calendar month from the date of their decision letter in which to appeal. You need to say why their decision is wrong, and provide evidence that shows what the correct decision should be and why.
If you got your decision much longer ago, you can still appeal up to 13 months later as long as you can show reasonable cause for the delay - but this has to be an exceptional reason such as death or serious illness, not just because you didn't know you could appeal. You will only be allowed to go ahead with a late appeal if they think you have a reasonable chance of success.
I would suggest getting helping from an advice agency to appeal.