that you haven't found it is mainly because it isn't Russian at all, the name has an Arabic origin. In the Arabic language, Lyaisan (this seems like the common to write the name) means 'showers' as in the verb 'to shower' (so not the plural of 'shower').
Famous person bearing this name is the Russian female gymnast Lyaisan Utyasheva. The problem with Russian names is that there is not really one way to write a name. So Laysan, Lyasan and Lyaisan all are excepted and you'll find that gymnast with all of the three variations. How an Arabic name is used in Russia is probably because it was used first by Tadzjikistan and Uzbekistan and such. Those are countries that have the Islam as religion and often use Arabic names in their culture. Probably Russian people took it over because they liked the name (like you do).
Hoped i helped you out :-).