I like to drink iced tea on shabbos. I like to add fresh lemon juice to the tea. A person can squeeze lemon into sugar, and put it into the tea. Can a person instead squeeze the lemon into a spoon and then add it to the iced tea?
No, although it is permitted to squeeze the lemon onto sugar, it is not permitted to squeeze lemon into a spoon.
The reason for this is that when lemon is squeezed onto a solid (such as sugar), we do not see it as though a liquid is being extracted from the lemon, since it is immediately absorbed by the sugar. When, however, lemon is squeezed into a spoon, one is extracted liquid from the lemon, and according to most authorities this is not permitted (because it is normal to drink lemon juice).
Sources: See Mishnah Berurah 320:22; Shemiras Shabbos Kehilchasa chap. 5 [but see Aruch Hashulchan 320:17, though it is probable that today, when lemons are commonly squeezed for juice, this ruling would not apply].