Nooooooooooo, not 'sissyluck'...! What are you thinking...!
...ha ha ha... seriously though cocinelle I don't speak one word of Thai and my only basis for analysis is ^ the YouTube clip. Don't trust me too much. But to me it sounds as if three of the speech sounds are pronounced slightly different than you would pronounce them in English.
The U in luck sounds to me as if she opens her mouth wider and/or broader than you would for the U in lucky luck, if you see what I mean. But she still does it very quickly, doesn't freeze with her mouth wide open, ha ha.
The K sounds softer to me than an English K, the way she says it it sound as if there's little or no aspiration i.e. no gush of air after the K, as there is in the English word luck.
Finally the R sounds different to me too, you're definitely right about that, but it's not an S sound. More like a Scottish R but with much less energy, much less "rolling".
Please remember this is just from listening to the clip and I don't really know what I'm saying, ha ha. Furthermore there will be dialects and sociolects in Thai as in every other language so no matter how well you prepare you may not say it the way she does... but I think it's lovely that you should try - names mean so much don't they.