Yes, it is correct, and I agree with Tony and Shawn. This sentence only works in British English, where the past participle of 'get' is the same as the past - 'got'. The answer is
"Tony seems TO HAVE GOT LOST on his way"
It doesn't work in US English, but don't worry - there isn't a mistake in your book. I also agree that 'while coming' and 'on his way' are a little unnecessary and unnatural, but sometimes test writers are forced to write some odd-sounding things to make the questions work.
By the way, I'm not only a native British English speaker, but I also write these tests as a profession, so you can take it from me - the sentence is fine.