Sorbets are sugar syrup (water and sugar simmered on the stove until dissolved) with juice. Adding milk or cream would make it more of a sherbet or gelato.
It's best not to add lemon juice or other juices as it is simmering as they lose flavor from being cooked. If the idea of frozen lemonade makes your mouth water, sorbet is worth making. I really need to get back to making sorbet more often.
For making sorbets, The Krups Automatic Ice Cream Maker (used to be called the Krups Glaciere) can't be beat for $50. it's compact, quiet, and easy to clean. Ideal for use on a counter. No rock salt required.
You just need sufficient freezer room to keep the empty freezable canister for 12-18 hours beforehand.