It's not abudnadantly clear where this word comes from. Since g often gets replaced by y in English, leisg is obviously similar to lazy. MacBain lists various somewhat similar words in various languages, without actually concluding what comes from where.
leasg, leisg, lazy, Ir. leasg, 0. Ir. lesc, W. llesg : *lesko-s ; Norse loskr, weak, idle, 0. H. G. lescan, become extinguished, Ger. erloschen (Stokes). Brugmann and others give stem as Hedsco-, comparing Got. latz, lazy, Eng. late, to which Norse loskr may be referred (*latkwa-z) ; root led, lad.
Geiriadur Pryfysgol Cymru defines llesg as
weak, frail, faint, languid, feeble, weary, infirm, sickly; faint-hearted, dispirited; ?tiring; lazy, sluggish, slothful, slow; poor, mean; low (of fire); weak (of drink), dilute(d).
but doesn't do any more than MacBain for the etymology.
For English lazy, Wiktionary is equally non-committal, saying
Attested since 1540, origin uncertain. Probably from Middle Low German lasich (“slack, feeble, lazy”), from las, from Proto-Germanic *lasiwaz, *laskaz (“feeble, weak”), from Proto-Indo-European *las- (“weak”). Akin to Dutch leuzig (“lazy”), Old Norse lasinn (“limpy, tired, weak”), Old English lesu, lysu (“false, evil, base”). More at lush.
An alternate etymology traces lazy to Early Modern English laysy, a derivative of lay (plural lays + -y) in the same way that tipsy is derived from tip. See lay.
For my money, I think (not being an expert) that y is more likely to come from g than u so lazy could well come from Celtic, even if related to the other words.
Now, as for leisgeul, no one expresses an opinion on that either. It sounds as if it could be related to leisg but it could also be related to sgeul 'story', related to Englsih spell and gospel. After all an excuse is a story you give to explain what you didn't do. Perhaps leisgeul is some sort of port-manteau: *leisg-sgeul 'lazy story'.
Yes it is a real pain when this happens. The system should allow some way out. One thing that sometimes works (if you are on a platform that allows this) is copying their correct answer and pasting it in when the question comes round again. Apart from anything else, this provides proof that it is not any kind of typo on your part, or the wrong symbol being inserted or anything like that.
If this was a tiles question then switching to the keyboard can help. If none of that works, then you just have to try doing the level test. You will lose 1 mark if the same question comes up, but it will not impede your progress.