Hi Shooby
Have a look in 'Members only Guide' 'ESA and UC'
www.benefitsandwork.co.uk/help-for-claimants/esa1 it gives a list of what qualifies to be placed in LCWRA group, unless your Obstructive Sleep Apnoea fits in with of these, then you will struggle to be placed in LCWRA.
You can automatically be treated as having a limited capability for work related activity if you:
a) have a terminal illness
b) are receiving chemotherapy or radiotherapy for cancer
c) are pregnant and there would be a serious risk to the health of you or your child
d) have a specific disease or bodily or mental disablement and consequently there would be a substantial risk to the mental or physical health of any person if you were found not to have a LCWRA
Gary