(n.) an especially comfortable chair
To lollock, or lallack, is to lounge around—which makes a lollockin a particularly comfortable chair in which to do precisely that.
That’s an entry from the English Dialect Dictionary (as well as a few others), which pinpoints it to the southwestern dialects of Warwickshire and Shropshire in particular.
Etymologically, lollockin is just an extension of the verb: if you lollock, then you’re lollocking, and from there the word has simply been clipped and restyled as a noun to produce lollock. As for the verb lollock itself, there’s an obvious connection here to the more familiar loll, meaning to move or position yourself in a relaxed, loose-hanging manner.
Are the two connected more overtly? It’s plausible, certainly; loll has been around since the 1300s, so it’s feasible that it might have been later extended to a more fanciful form in regional language. But it’s equally possible these two are unconnected, and united merely coincidentally by the expressiveness of those neighbouring L sounds (a phenomenon properly known as phonosematics—the almost onomatopoeic way in which certain sounds seem to vividly match or evoke a meaning).
In this case, there’s something about the way the “l” sound is produced that makes it seem particularly appropriate for the languishing, lounging feeling of lolling and lollocking. (Lull and lullaby both fit this bill too, and derive from earlier words for rocking a child to sleep.) It could simply be the case, then, that lollock is its own word, driven by the same phonosemantic association that gave us loll and lull as well.