A trick I often do to simulate this, is using alternating sublines [%t() tag]. It's not *exactly* the same, but it's fairly close. In the 3 lines case you mention, it would be something like this:
First line, scroll for 8 seconds (or your preferred interval), don't scroll for 16 seconds
Second line, don't scroll for 8 seconds, scroll for 8 seconds, don't scroll for 8 seconds
Third line, don't scroll for 16 seconds, scroll for 8 seconds
As you can see, no line will scroll simultaneously with another.