from Dictionary Reference
laik /leɪk/ verb (Northern English, dialect) 1. when intr, often foll by about. to play (a game, etc) 2. (intransitive) to be on holiday, esp to take a day off work 3. (intransitive) to be unemployed Word Origin C14: leiken, from Old Norse leika; related to Old English lacan to manoeuvre; compare lark
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
"spree, frolic," 1811, possibly shortening of skylark (1809), sailors' slang "play rough in the rigging of a ship" (larks were proverbial for high-flying), or from English dialectal lake/laik "to play" (c.1300, from Old Norse leika "to play," from PIE *leig- "to leap") with intrusive -r- common in southern British dialect.
The verb lake, considered characteristic of Northern English vocabulary, is the opposite of work but lacks the other meanings of play. As a verb, from 1813. Related: Larked ; larking.
looks like a very solid connection to modern Swedish leker
Online Etymology Dictionary, © 2010 Douglas Harper
laker to lark about, to play - not sure if "lark" is used where you live/have lived attis765, it is not commonly heard here in Oz these days, though it might be the basis of the word "larrakin" = street hoodlum, mischievious youth, which is still commonly understood here
Spelar related to the English word "spiel" which derives from the Germanic word to play. Spiel - noun 1 a usually high-flown talk or speech, especially for the purpose of luring people to a movie, a sale, etc.; pitch. verb (used without object) 2. to speak extravagantly.
it might have the idea of play with words, exaggerate, a bit like playing with a ball. Not sure this will help you to remember but I hope it is useful.
Barnen leker tjuv och polis - 'The children play thief and police' – not that kids do that anymore, but back in the old days when kids used to play games like that, the verb was leker because it's a pretend game without real rules.
Katten leker 'The cat is playing' – animals typically leker unless maybe if you can make your cat play games on your iPad. :)