I've actually been reading a lot today about how the 'lame/crippled' meaning is probably incorrect. This comment I stole sums it up, although of course could be wrong:
"The name Claudia is actually related to power and protection, both historically and etymologically.
It is quite obvious that such a popular name, especially among the elites of the Roman Empire, did not mean a weakness at all and it is surprising that the meaning "lame" is still perpetrated across so many websites. However, this perpetration is understandable, as online content is often copied from one source to another.
Claudia derives from Claudius, which comes from the Sabine name Clausus, which means closed, inaccessible, sealed or unreachable, and was used in contexts such as "fenced land" (property). Claudius is the romanization of Clausus and originated with the legendary founder of the Roman Empire, Appius Claudius Sabinus Regillensis, who was originally called Attius Clausus.
Appius Claudius (505 - 480 BC), the empire founder, was born long before Claudius (10 BC-AD 54), the emperor who was believed to have some kind of disability. So the name obviously precedes the famous disabled bearer, both in History and in his personal life, since his disabilities did not manifest at birth or in his first years of life, so he was not named after them. Rather, the name he received was a great status symbol and did not relate to disabilities at all.
Appius Claudius, the empire founder, was the first famous bearer of the name Claudius and the leading figure of the aristocratic party in the early Roman Republic. Claudius and Claudia were always noble names and status symbols.
The name Claudia has been mistakenly associated with the Latin claudicus (to limp or waver), since such an honorable and desired name could not have had a bad meaning as it was a hit with Latin-speaking people, who were perfectly aware of all its possible meanings. (Even freed slaves would voluntarily keep this name, given by their former owners.)
Coming from clausus (as in Attius Clausus), the name is actually related to the verb claudo, which means to close, conclude or lock. So the name Claudius probably appeared with a sense of land ownership that, back then, was strongly related to the ability to protect the land. That makes a lot of sense with the exact timing of the birth of an empire (the Roman Empire, founded by Appius Claudius).
When the powerful Appius Claudius founded the Roman Empire, the name Claudius was such a desired name that people who could not use it as a surname (first form of the name), began to use it as a given name. For such a desired and popular name, the meaning of "lame" does not make any sense, at any time.
The name Claudia obviously follows the meaning of enclosure (to seal an area with a barrier; for example, a fenced land) and could even be related to the English “to close". Considering its history, it is clearly related to the protective power of a fortress and, therefore, to the fortune it protects. One could easily add the meanings of a safe haven or a safe home. The idea of "protection" was probably in the meaning of the original Roman name, as the name was an "elite" name, a name for “inaccessible”, "protected" people.
Other popular names also have ambiguous/negative meanings in their roots, e.g. Amelia, Emily, Cecilia and Deirdre, just to name a few. However, it seems that they have received new meanings in recent times and the "bad meanings" are fading away. In the end, it is the culture we live in that counts, and today these names are joyful and beautiful. Claudia's mistaken meaning is also fading as more researchers, and History, join the discussion. Anyway, it is always a distinctive, beautiful, and powerful name.
So, for all Claudias out there: Claudia means “to enclose” in the sense of keeping/protecting, originally wealth/properties. In short, it expresses protection and power.
And it sounds great."
And this reassured me for about 5 minutes HOWEVER i'm not sure that this is something I could be bothered to learn off by heart and try to explain every time I introduced a new baby. Like, "This is Claudia, and I know what you're thinking, Claudia means lame or crippled, right? BUT WAIT! ........" And then into the entire speech.
Might save time just to choose another name.