My aunt is currently visiting the USA, but now has a need to visit London. Is it possible for her to get a visa to the UK while in the USA, and if so how? Or must she return to India to get a UK visa?
There is no requirement to submit an application for a VISITOR visa in the applicant's home country, otherwise the system would be subject to challenge on the Wednesbury principle. In many cases, the application is referred.
She would apply on the net just as she would in India. Because India is a visa-national country, your aunt may not qualify for the express service, and certainly the standard turn-around would not apply either. So there's no point in paying the extra fees because they will not be refunded and the application will be referred anyway.