If you don't care who you fly, there's a lot around $800 throughout July.
$728 Example:
Los Angeles, CA to Bangkok, Thailand: 8328 miles 19 hrs 50 min
Delta Air Lines Flight DL9875 on a Boeing 747 (jet) in coach class
(operated by China Airlines as Flight CI 7)
(breakfast)
Departs Los Angeles, CA (LAX) Mon, July 26 1:15a 13 hrs 15 min
Arrives Taipei, Taiwan (TPE) Tue, July 27 5:30a
1 adult in booking code Q, covered by fare (A1) below
Layover in Taipei 3 hrs 0 min
Eva Airways Flight BR211 on a Boeing 747 (jet) in coach class
(meal)
Departs Taipei, Taiwan (TPE) Tue, July 27 8:30a 3 hrs 35 min
Arrives Bangkok, Thailand (BKK) 11:05a
1 adult in booking code B, covered by fare (A1) below
Note: The flight from Los Angeles (LAX) to Taipei (TPE) is overnight.
Note: You must change terminals in Taipei (TPE).
Bangkok, Thailand to Los Angeles, CA: 8328 miles 19 hrs 40 min
China Airlines Flight CI 66 on a Boeing 747 (jet) in coach class
(meal)
Departs Bangkok, Thailand (BKK) Mon, Aug 2 8:25a 3 hrs 35 min
Arrives Taipei, Taiwan (TPE) 1:00p
1 adult in booking code H, covered by fare (A2) below
Layover in Taipei 3 hrs 40 min
Delta Air Lines Flight DL9872 on a Boeing 747 (jet) in coach class
(operated by China Airlines as Flight CI 6)
(dinner)
Departs Taipei, Taiwan (TPE) Mon, Aug 2 4:40p 12 hrs 25 min
Arrives Los Angeles, CA (LAX) 2:05p
1 adult in booking code Q, covered by fare (A2) below
Note: The flight from Taipei (TPE) to Los Angeles (LAX) is overnight
If you want United, here's one for $824:
Los Angeles, CA to Bangkok, Thailand: 8321 miles 19 hrs 55 min
United Airlines Flight UA891 on a Boeing 747 (jet) in coach class
(lunch, movie)
Departs Los Angeles, CA (LAX) Tue, July 20 12:55p 11 hrs 5 min
Arrives Tokyo, Japan (NRT) Wed, July 21 4:00p
1 adult in booking code V, covered by fare (A1) below
Layover in Tokyo 2 hrs 25 min
United Airlines Flight UA837 on a Boeing 747 (jet) in coach class
(dinner, movie)
Departs Tokyo, Japan (NRT) Wed, July 21 6:25p 6 hrs 25 min
Arrives Bangkok, Thailand (BKK) 10:50p
1 adult in booking code V, covered by fare (A1) below
Bangkok, Thailand to Los Angeles, CA: 8321 miles 17 hrs 15 min
United Airlines Flight UA838 on a Boeing 747 (jet) in coach class
(breakfast, snack, movie)
Departs Bangkok, Thailand (BKK) Wed, July 28 7:00a 6 hrs 10 min
Arrives Tokyo, Japan (NRT) 3:10p
1 adult in booking code V, covered by fare (A2) below
Layover in Tokyo 1 hr 15 min
United Airlines Flight UA890 on a Boeing 747 (jet) in coach class
(breakfast, dinner, movie)
Departs Tokyo, Japan (NRT) Wed, July 28 4:25p 9 hrs 50 min
Arrives Los Angeles, CA (LAX) 10:15a
1 adult in booking code V, covered by fare (A2) below
Note: The flight from Tokyo (NRT) to Los Angeles (LAX) is overnight.