A dedicated battery is not necessary at all. I run my smaller gassers - dle20 - with just 1 batt feeding the Rx n CDi.
What I like to do is to have 2 swithes....1 fr Rx n other fr CDi. In the wire fom the switch to the CDi I attach the diode.

And yes this works for Life only. for LiPo you will need more diodes, in which case an Ibec may be better.

But I will highly reccomend Lfe for CDi as they give a constant voltage over 80% of their life.