Hi Moana, welcome to TP
The problem is that having a diagnosis tells you nothing about how that person is or how they will react, years ago my wife could be driven round in the car for ages and it made her happy, then one day she decided she wanted to get out at about 50 miles per hour.
In an aeroplane you're in a very vulnerable position, if anything goes wrong and it's likely the crew will have had no dementia training then likely as not they'll treat her as being "a danger to the aircraft" and if they have to divert and do an emergency landing they could send you (or your insurance company) the bill.
California to London is about 6,000 miles then London to India and you're literally flying half (or more) round the world anything could happen, what happens if you go to sleep and they wake up, will the aircrew be able to cope?
If I were you I'd make sure you had all the right insurance in place as if anything did happen like an in air incident a divert to another country or even a medical emergency I'd make sure you were covered for any costs of a divert or medical treatment anywhere you might be overflying.
There's a massive possibility of disorientation and jet lag is just one, passing through airport security, boarding a plane and the whole disorientating experience of such a long series of flights could trigger many more issues than just jet lag.
You use the word "patient" which might (?) imply that this isn't a family member and "caregiver" could be a family member or someone being paid to do a job, whatever the circumstances I'd make sure you had a good backup plan if anything, anywhere goes wrong and remember that the American's tolerance to anyone behaving oddly on a plane can be dealt with by an on board armed officer and that includes American airlines flying both to and from the USA as well as internal flights.
As I say someone with dementia doesn't mean a lot, it could be mild, moderate or severe but I'd want worldwide health insurance (for both or you\) for the duration of the trip and as well as plan A I'd want plan B,C and D in place too, just in case you became ill, it happens a lot when people go abroad, who'd take over you became suddenly ill, it can happen?
K