By Rabbi Dovid Ostroff
Is one permitted to squeeze lemons in order to make lemonade on Shabbos?
In the first instance we would say that it is forbidden, because in previous shiurim it was explained that when people squeeze fruit for juice, it is forbidden for everyone to do so. The Beis Yosef  himself was perturbed by this as he says that the people of Egypt were accustomed to squeezing lemons into sugared water and the sages did not remonstrate against them for doing so.
Accordingly the Beis Yosef offers two explanations why it should be permitted:
The first being that the prohibition of squeezing fruit only applies when the beverage is consumed undiluted, but when always mixed with another beverage it is permitted.
The second being that squeezing fruit is prohibited when squeezed into an empty cup but is permitted when always squeezed into a beverage.
Lemons in Egypt were always squeezed into sugared water and therefore that custom complies with both explanations.
Nowadays however lemons are squeezed into empty containers as well and therefore should it not be forbidden to do so?
Correct, the Mishna Berura himself points that out. The M”B  says that since nowadays lemons are squeezed to fill barrels in the thousands and only later is the juice mixed with sugared water and the like, one must squeeze lemons onto sugar  and add the concoction to water. (As to the amount of sugar required for this method, we will soon see). He does not permit squeezing lemons into an empty cup or into water. The Kaf haChaim  brings many other poskim who prohibit squeezing lemons on Shabbos to make lemonade and he also advocates squeezing the lemon onto sugar and then adding it to water.
Does that mean that I am forbidden to squeeze a lemon into my tea on Shabbos?
I am afraid so because one is squeezing a fruit into a liquid and therefore the squeezed juice is classified as liquid and forbidden. The modus operandi would be either to squeeze a lemon onto sugar and add the sugar to the tea or to squeeze lemons before Shabbos and add the juice to tea on Shabbos.
When squeezing lemon onto fish or salad, how much of the juice must be absorbed into the food?
The lemon that is squeezed onto fried fish is absorbed into the fish and therefore it is considered as separating a food from food. When squeezed onto lettuce salad, for example, it is not absorbed into the lettuce but since it enhances the lettuce, it is permitted.
We find proof in Hilchos Yom Tov that such an action is permitted. The Mechaber deals with the problem of milking on Yom Tov, which as we know is a Biblical prohibition. The proffered solution  was to milk onto bread, by which the milk is absorbed into bread thereby utilizing the rule that says that squeezing onto food is permitted.
Obviously it would be ineffectual milking 10 liters of milk onto one slice of bread, but when the majority of milk is absorbed in the bread this solves the problem.
The next solution was to milk onto food that would be enhanced by the milk. Here too the Mishna Berura  says that it suffices if the majority of the milk enhances the food.
We see that the liquid does not have to necessarily be absorbed into the food – suffice that it enhances it. Therefore we are safe to say that one may squeeze lemons onto lettuce salad. 
If we revert to our case of squeezing lemon onto sugar, the halacha is that the majority of the squeezed lemon must be absorbed into the sugar. It would not help to squeeze an entire lemon onto a few grains of sugar. If one requires more lemon one must use more sugar.
What is the halacha with regards to squeezing the excess liquid from a pickle?
The reason for prohibiting squeezing a fruit for its juice is because one ascribes importance to the extracted juice and promotes it from being a food to a beverage.
Were one to squeeze out the juice for a different reason the ramifications would be different.
Pickles are often saturated with excess brine or vinegar and one’s sole purpose when squeezing the pickle is to rid it of the excess liquid. Since one is not squeezing it for the sake of its juice, it is permitted.  One may even squeeze it into a cup or plate;  it need not be squeezed into a tissue or napkin.
The Mishna Berura  says that the same halacha applies when squeezing lokshen from excess fat or lettuce after being soaked in water. The purpose for extracting the liquid is not to produce a beverage; rather it is to rid the food of excess liquid.
Does that mean that one may squeeze fruit to rid it of its excess liquid?
The Mishna Berura  writes that one may not squeeze olives and grapes in order to rid them of excess juice, because one might easily squeeze them for their juice. This implies that one may squeeze all other fruit to rid them of excess juice.
According to some opinions,  one should refrain from squeezing juice from oranges for the very same reason.
 Page 434 in the Machon Tur 5 lines from the bottom.
 M”B siman 320:22.
 The Chazon Ish in siman 56:7 disagrees with this solution saying that if the intention is to drink the lemon juice it does not help to first squeeze it onto sugar.
 Siman 320:36.
 See the Shulchan Aruch in Hilchos Yom Tov siman 505:1 and M”B 6.
 M”B siman 505:5.
 See the SS”K 5:7.
 Siman 320:7.
 M”B siman 320:24-25.
 End of M”B 320:24.
 This is based on the Rashba who writes that grapes and olives are d’oraisso because most of the fruit is squeezed for its juice. Accordingly, since today most oranges are squeezed for their juice, squeezing oranges on Shabbos to produce a beverage involves a d’oraisso.