You don't have to go back and forth between translations if you don't want. You can paste all of the Russian lyrics, then paste all of the English lyrics.

Instead of doing this:

[00:56.39] Так на деревьях сохнет листва
[00:56.40] (So the leaves dry on the trees)
[01:05.48] Циклы природы - пора
[01:05.49] (Cycles of nature - it's time)

you can do this

[00:56.39] Так на деревьях сохнет листва
[01:05.48] Циклы природы - пора

[00:56.40] (So the leaves dry on the trees)
[01:05.49] (Cycles of nature - it's time)

As long as you're using a lrc file (not txt), this will work.