Regarding the definition (Geder) of what a liquid is:
The Shulchan Aruch HaRav writes in Seder Bircat Hanehenin 8:8
אוכל שנימוח כ״כ עך שראוי לשתייה - יצא מתורה אוכל. וכן:משקה שנקרש עד
שראוי לאכילה - יצא מתורת משקה - אפי' יש בו טופח ע״מ להטפיח
(And in my own free translation:)
A food which has dissolved to the extent that it is suitable to drink
it - it ceases to be food (and becomes a liquid)
Similarly, a liquid which has congealed to the extent that it is
suitable to be eaten - ceases to be a liquid - even though it is still
somewhat wet.
So it depends on how you would consume the 'slush':
If you eat it - which would involve processing the food with your mouth like chewing or sucking (like on hard candy) - the it's a solid [see Minchat Yitzchak Vol2 Siman 110
], however, if you drink it - then it's a liquid.
(Presumably it would be a liquid - as you generally drink slurpy's and the like with a straw)
Just for completeness:
Even though the Mishna Brurah seems to permit squeezing the lemon on the sugar without extra conditions being met, there are other Poskim which only allow this when
1) All the lemon juice is absorbed into the sugar (with no excess liquid) -
[ Chazon Ish Siman 56 S"K 1
]
2) You want to eat the sugar/lemon mixture (and,say, only add a little exra liquid).
But if you're planning to eventially make a lemonade out of it - it's forbidden as if he initially sqeezed it on liquid. [Chazon Ish Siman 56 S"K 7
, Ktzot HaShulchan 126 S"K 19
]