Used on both the first and second American tours and in the studio for LZII. Though Page says he thinks he used a Super Beatle on LZII, this is actually the amp he is likely referring to for some of the tracks. He says he acquired the Super Beatle amps during The Yardbirds, but there is no evidence of him using a Super Beatle during the Yardbirds. However there is evidence of a Vox UL4120 in April 1968. Probably the most substantial evidence for this being used on some LZII tracks is it being spotted during sessions for the second album in May and June '69, particularly it being seen at Olympic Studios in June 1969. What Is and What Should Never Be and Whole Lotta Love were both recorded there according to the album notes, you'll notice a very similar tone between the two as well. Whole Lotta Love was one of the songs Page says he thinks he might have used the Super Beatle for. How much use the amp saw elsewhere on II is up for debate, but it was likely main amp used.
The UL4120 is a hybrid amp, the preamp is solid state and it has a KT88 power section along with a tube driver section that uses two ECL86 tubes. The 4120 was the bass series of the UL series amps. The 4120 lacks the reverb and vibrato of the 7120 model, along with the built in fuzz. There also is a small input capacitor change and a different value for the mixing resistor. Other than that the amps are rather similar. More technical specs here: http://voxshowroom.com/uk/amp/7120tech.html
In the 1990's Page also bought a few 7120s which can be seen in It Might Get Loud, so he definitely seems to have a fondness for these amps.
April 1968 - With the Yardbirds
February 1969 - Thee Image Club - Miami
May 1969 - Rose Palace
May 1969 - Though the amp isn't in full view, the handle can be made out at the far left. Studio is believed to be Mirror Sound or Mystic Studios
June 1969 - Olympic Studios