In the originals, yeah. But they changed it to Tea in the remakes, thanks to the whole Held Items thing.
If they'd left the required drink as Lemonade, then it would've been possible to give Lemonade to a Pokemon and then trade it to a new game, allowing one to access Saffron City before they even battled Misty. In order to prevent such Sequence Breaking, they changed the required drink to Tea, which is a Key Item and cannot be held by Pokemon.
I always assumed that it was a flask of tea, like you'd take on a picnic, since you could put it in your bag without it spilling everywhere and getting cold. A flask would also contain enough tea for multiple cups, so could be shared.
i always wondered how one cup of tea (certainly cold when i get it to them finally) is enough for four gaurds, and the one guard i give it to is going to walk to each of the other guards and share that small cup of tea! XD i also wondered what gives them the authority to tell me i cant pass just because they are thirsty for tea XD