When you dissolve an ionic compound into water, the have a tendency to separate from each other. They're still chemically the samething.
LiOH is an ionic compound. Lithium is positive and "borrows" the hydroxide's negative charge to be neutral & vice-versa. When LiOH is dissolved in water the Lithium and the hydroxide separate into their respective forms, also known as ions.
So, LiOH dissolves to become these ions in solution= Li+ and OH- (the plus and minus represent their charges).