Richard Rodgers and Stephen Sondheim are the subjects of major biographies by the same author, Meryl Seacrest (sp?).
There was a bio of Hammerstein published in the mid-70s.
Rodgers died in 1979 and Lloyd Webber probably had little if any contact with him.
Runnicles is correct in that Lloyd Webber is not American and his shows often lack the grand passion of US written shows. (The reason Phantom works on an emotional level is Hal Prince. Evita, with the same director, does not really.)
Actually Hal Prince (who thinks operatically) is by far the larger connection for these two writers than R&H. And also if you are writing about lloyd Webber then you have to consider the various lyricists with whom he has collaborated.
There are many books on Sondheim and Prince and the best place to check might be the above-mentioned Sondheim bio's bibliography.
In addition to Amazon.com, there is also Abebook.com (I think that's it) that deals in used books. Also a decent library may have some books or quite frankly, your friendly local show queen might have the best library of all.
A final bitchy observation: Lloyd Webber is not just influenced by Puccini, he lifted a musical phrase right off the page of The Girl of the Golden West and plugged it into the Music of the Night. ["Turn your head away from the naked light of day"...etc."] Anecdotally there was supposed to be a nice chunk of change that got paid to the Puccini Foundation for that 'sampling'.
Also the homage to 'Come to Me, Bend to Me' from Brigadoon in the same score is just that. Alan Jay Lerner was originally set to do the book and lyrics to Phantom, but died before they barely got started.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher