You are correct that people often checked themselves into the workhouse infirmary for free medical treatment. Unfortunately in Lisnaskea’s case the admission records don’t appear to exist. They would have told you when your ancestor was checked in and out and a bit about her circumstances. However there is some general information about Lisnaskea here, and the Board of Guardians Minutes will tell you a bit about life there. (They met weekly and contain the usual management information about how many inmates there were, illnesses food, purchases significant incidents etc). They are in PRONI in Belfast. (They are not on-line).
https://www.workhouses.org.uk/Lisnaskea/
Lisnaskea workhouse still exists and there have been some calls for it to be made into a museum. My own family lived in it for many years after it ceased to be a workhouse. (A small part of it was converted and used for conventional accommodation for many years).
Think of the workhouse as the Victorian equivalent of modern social welfare. It provided a basic safety net - accommodation, food and work but was fairly strict and for most folk was somewhere to get out of if they could but the ill, elderly and very poor sometimes had no other choice. It could be grim but the minutes and Masters Journal sometimes indicate humanity at work. In the Master’s Journal you will sometimes read that a resident had been allowed out to go to a funeral but had come back drunk. That sort of thing. In Ballymena workhouse, in the late 1840s, the young ladies had been found opening windows high up in the building at night, and young men of the town, accompanied by bottles of whiskey, had been leaning very tall ladders against the outside wall and then climbing up for a social visit. Life goes on, even in the hardest of conditions.
Sponsor in the case of a baptism means godparent.