The Algae color for manes is a Breed-Only trait. So to have a lion with it, it would have to have been passed down to them from one of their parents.

I did a quick search on the trading center for lions with Algae colored manes, are there are a few available. I wasn't sure if you're looking for a male or female, or what age, so the search is just for lions with Algae manes - see below.
https://www.lioden.com/trading_center.php?s=lions&keywords=&owner=&personality=&gender=&level_type=min&level=&flevel=min&fertility=&age_min=&age_max=&sb=&gb=&lco=min&lcv=1&mane=&mc=522646479&eyes=&skin=&basecolor=&basegroup=&baseshade=&basegradient=&baserarity=&mutation=&mk_cg=&cg_slots=&mk_tg=&tg_slots=&tmo=&tm=&mk1=&mk1s=&mk2=&mk2s=&mk3=&mk3s=&mk4=&mk4s=&mk5=&mk5s=&stattype=min&str=&spd=&sma=&skl=&agi=&stats=#results

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Its breed only, so the lion has to be born with it. It's on the Manes section of the wiki.

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To answer your edited question, I believe it originally started with a Raffle Lioness. Specifically, the raffle lioness on 12/30/2022 was the first one, I believe, and there's been a handful of other raffle lionesses that have had the Algae mane color since.

Below is the link to the News that announced that she was the first Algae maned lioness:
https://www.lioden.com/topic.php?id=304429484353

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