Why is lunatic party recommend over Doppler part for getting the CE

They have the same CE drop rate: 1%.

The droprates are the same. It is just the lunatic is much easier to farm with. In Doppler, the cu's tend to spam evasion if you cannot kill them in one round, and the last wave are two rulers. The royal one has three rare powerful servant in the last wave.

That said, it depends a lot on your setup. I got mine from the doppler as I have a good avenger.

Hmm not much of a challenge as long as you have at least 1 aoe zerker. Sparteus is great for this. If you managed to pull a Tama cat from this gacha, she clears last wave easily.

My 3 team -

Arash - kscope, maxed 3rd skill
Tamacat - devil illya CE
Support waver
Sparteus - devil illya ce, lvl6 guts skill

I use zerker team mostly on Halloween event.
Hercules, Tamamo Cat, Ibaraki, Lu Bu, Kiyohime, and friends berserker.
Mostly they died when get hit 1-2 times by using Buster card and some atk buff.