If you are arriving at LAX on UA, you will have to take a shuttle bus from Terminal 7 to the customs/immigration area at the Tom Bradley International terminal. It's total hit or miss at customs/immigration, all depending upon the number of international flights arriving at the same time.
As stated above, you will then have to either take a shuttle bus to Terminal 1 to cach your US flight, or -- better yet -- just walk across the parking lot to Terminal 1, which is directly opposite terminal 7.
As stated above, the security line in Terminal 1 can be very long, sometimes extending back to Terminal 2. Other times, there is no wait at all.
I personally would not schedule such a tight connection if there is an option for a later flight, but if it is a choice between taking that connection or spending the night in Los Angeles, I guess you can chance it and keep your fingers crossed.
I'm flying back from FCO on CO on May 9. CO offered me the option of connecting to the last flight of the day back to LAX. With only 1.5 hours to clear customs/immigration and re-clear security, I did myself a favor and instead booked myself on the first flight from EWR-LAX the next morning.