Who in Greek mythology lived in a tub?

I cannot reference a character of Greek mythology that reputedly "lived" in a tub. I have discovered that Sciron had a special tub in which he made each passing stranger wash his feet. While they were engaged in this sanitary activity, Sciron kicked them over a cliff into the ocean below, where they were devoured by a man-eating turtle. Theseus turned the tables on Sciron, just as he had turned them on Pine-Bender.

http://www.chuckpalahniuk.net
http://www.mythweb.com/encyc/entries/theseus.html

Similarly, the Greek mathematician and philosopher was connected with a tub. One day as Archimedes was lowering himself into one of the public baths in the city, he noticed that some water flowed over the sides of the tub. It is said that he became so excited that he ran out of the bath house through the streets of Syracuse, yelling, "Eureka! Eureka!" In Greek it meant, "I found it! I found it!" Mind you, Archimedes was not a mythical character.

http://www.light-science.com/bathtub1.html

As BRY2K says, there doesn't seem to be a reference to any mythological Greek characters who lived in a tub.
However, the philosopher Diogenes was renowned for living in a public tub or water trough as an expression of his ascetic principles.

Once in Athens, Diogenes famously took a tub, or a pithos, for an abode. In Lives of Eminent Philosophers, it is reported that Diogenes “had written to some one to try and procure a cottage for him. When this man was a long time about it, he took for his abode the tub in the Metroön, as he himself explains in his letters” (Diogenes Laertius, Book 6, Chapter 23). Apparently Diogenes discovered that he had no need for conventional shelter or any other “dainties” from having watched a mouse. The lesson the mouse teaches is that he is capable of adapting himself to any circumstance. This adaptability is the origin of Diogenes’ legendary askçsis, or training.

http://www.iep.utm.edu/d/diogsino.htm

There is also a legend that Alexander the Great, who admired Diogenes' philosophy, upon hearing of his circumstances, travelled to visit him and asked if there was anything he could do to help him. Diogenes reportedly replied, "Yes, you can stand aside. You're blocking my sunlight."

The closest to what you're asking about as I can think is the sun-god Helios, who lived at the eastern edge of the Earth in a palace which stood in a bog of the Okeanos River, which river encircled the entire world. From this palace Helios arose each morning driving his fiery chariot drawn by a team of flaming horses, and together they would journey across the Sky to descend back into the Okeanos in the western extremities of the world at the end of the day. From here, every night, Helios would travel asleep, together with his fiery chariot and flaming horses, in a gigantic golden cup or bowl, in which he floated from the western Okeanos back to his palace in the eastern Okeanos to begin the cycle again.

Since Helios spent his daily downtime (= the duration of an entire night) in a cup or bowl, which he used more like a tub than cup or bowl, I don't think it would be inaccurate to say he lived in this golden vessel, in which he spent more time than at his golden palace. Granted there is the version which says that he slept on a golden bed afloat on the Okeanos on his nightly eastward way but maybe this just means that the bowl (or cup or tub) was furnished with a bed for the god too.