Imagine you work Mon, Wed, Fri and you have the opportunity to attend a training course Wed-Fri. You have to work the Thursday as you're on the course, so you book off a day in lieu later in the year, maybe take a Friday off.
Then the week of the course arrives and you are very sick and the GP signs you off work for a week. You have to cancel your attendance at the course.
What is the situation re. Time in lieu for the Thursday you were planning to work but couldn't due to sick-leave? Do you now take it out of your diary and work the Friday as normal?
I would probably work the Friday - but I think that if you are sick on a day when you are supposed to be working (i.e. the Thursday) then technically you were off sick on a normal working day so should still get you day in lieu?
Your time in lieu is for hours worked. You didn't work them, so you don't get it. Otherwise some people would be able to commit to working extra days for lieu, call in sick, get that day off AND a lieu day on top. Would be open to massive piss-taking.
Your company might, however, consider paying you sick pay for the day as you had agreed to be in. Of course then it would be added to your sickness record which you might not want. They might not, however, depends on their policies I guess.
Time off in lieu - is just that. You have not worked any extra and therefore there is no time off in lieu to take. Unless of course your contract of emplyment says differently and lays out more favourable terms.
if you are sick when you are booked to be on holiday then you can take that day as sick rather than holiday - whether you are paid at full rate for this would depend on your employers policies - we get 5 sick days a year, any extra above that are unpaid (apart from any SSP if the criteria for that is met).
On the specific TOIL question asked in the OP, I would think as others have said that TOIL is only for hours you have worked, and in this situation you haven't worked. Also as others have said, you were planned to work that day, you were sick, and so should get sick pay for it (if you qualify).