Looks good.

I think this is clearer.

@@ -17 +17,2 @@
-<gloss>person whose luck/happiness one wishes one had</gloss>
+<gloss>enviably fortunate person</gloss>
+<gloss>person whose happiness is the envy of others</gloss>

I think the last edit went wrong?

@@ -17 +17 @@
-<gloss>happy person who wants to share their happiness</gloss>
+<gloss>person whose luck/happiness one wishes one had</gloss>

Koj: その幸福にあやかりたいと思うほどのしあわせ者。また、ある幸福な人と同じような幸福を得た者。果報者。
Daijr:他の人があやかりたいとうらやむほど幸せな人。果報者。
Daijs: 他の人があやかりたいと思うほどの幸せな人。また、同じ果報にめぐりあった幸せ者。

I think one sense is enough. It's very rare. Only Daijisen hints at two senses.

@@ -15 +15 @@
-<xref type="see" seq="1351450">肖る・あやかる・1</xref>
+<xref type="see" seq="1351450">あやかる・1</xref>
@@ -17,6 +17 @@
-<gloss>someone whose good fortune one wishes they could share</gloss>
-</sense>
-<sense>
-<pos>&n;</pos>
-<misc>&rare;</misc>
-<gloss>someone who has come to share the good fortune of another</gloss>
+<gloss>happy person who wants to share their happiness</gloss>

See first: changes to 肖る

肖り者
daijs: 
他の人があやかりたいと思うほどの幸せな人。また、同じ果報にめぐりあった幸せ者。

daijs for 肖る
１ 影響を受けて同様の状態になる。感化されてそれと同じようになる。ふつう、よい状態になりたい意に用いられる。「彼の幸運に―・りたい」

あやかりもの	132	56.7%
あやかり者	0	0.0%
肖り者	0	0.0%

https://dictionary.goo.ne.jp/word/en/肖る/#je-1783
私も彼の幸運にあやかりたい
I hope I will 「have the same good luck as he [share his good luck].


=== A good twitter entry.  "lucky person" would not work. "I want to be a person who shares in this plan"
素敵な企画です💦ぜひ恩恵のあやかり者になりたいです(*´Д｀)前向きになれる世の中に明るい話題をありがとうございます

Also twitter (note that the luck and prosperity are tacked on explicitly)
幸運の象徴のあやかり者として崇められてただろ

The tweet below contrasts two types of people, a good 肖り者, and a bad  吸血鬼(blood-sucking demon). Surely "lucky person" isn't right here either - rather, someone worth of emulation?
https://twitter.com/_KO_METAL/status/1307285331616522241
世界には二つの選択肢があると思います

人の幸せを分かちあえ生きる肖り者
人の不幸を啜って生きのびる吸血鬼

キミは一体どちらなんだい？

Question about Japanese
Is 肖り者 a common word?
https://hinative.com/questions/13978647?feedbackable=true&pos=1&utm_content=search_questions_index&utm_medium=referral&utm_search_language_id=45&utm_source=hinative&utm_term=肖り者
"people are envious"
I think that words with this nuance do not exist in modern Japanese.

if you say...

"幸せ者" siawase-mono (happy person)

Japanese people can understand "Lucky".
You can communicate English words.

"ラッキーボーイ" (Lucky boy)
"ラッキーガール" (Lucky girl)
ーー
When I want him to share his happiness:
「肖りたい！」(ayakari-tai)
肖る share somebody's good luck
たい want

====

肖り者 (ayakari-mono) is not a common word.
肖り者:
A person who is so happy that people are envious.

@pompomriver Ah I thought it meant a lucky person lol
What's a common way to say that someone's always lucky?
....

See first: changes to 肖る

Super rare, but a few hits on twitter.

Because it is super rare, there's not much practical need for a compact gloss.  I think it's better that if someone actually looks this term up, that they understand the nuance of what is being said.　　(In fact, it doesn't seem so off from a simple 羨ましい, and I've seen these two terms paired).

Instead, the long-winded gloss I've given better reflects the meaning of the kanji ("resemblance", nothing at all to do with luck), and removes the mystery of why this term exists.

One should never think 肖り者 is a good term for "lucky person" (as one hinative poster did).  Even if concern for J->E is secondary, complicating the gloss eliminates this risk.

Note the terrible tatoeba E->J gloss:
彼はたいした肖り者だ。
What a lucky person he is! - Tatoeba例文

gloss [2] is right out of daijs.

As a super-simple gloss, could do "enviable person" for [1] I guess. To me it does more harm than good (English speakers generally shouldn't use 肖り者, and we're also unlikely to need the gloss given the rarity of this term.  And, as an exclamation (as I've seen on twitter), it's still a stilted gloss anyway).

Found this on twitter. あやかり者 might mean "idiot" in some dialects. I think I saw some twitter uses where this seemed to be the case
日本でも方言で「あやかり者」がしばしば馬鹿を意味します。

@@ -5 +5 @@
-<keb>肖り者</keb>
+<keb>あやかり者</keb>
@@ -8 +8 @@
-<keb>あやかり者</keb>
+<keb>肖り者</keb>
@@ -15 +15,9 @@
-<gloss>lucky person</gloss>
+<xref type="see" seq="1351450">肖る・あやかる・1</xref>
+<xref type="see" seq="1351450">肖る・あやかる・1</xref>
+<misc>&rare;</misc>
+<gloss>someone whose good fortune one wishes they could share</gloss>
+</sense>
+<sense>
+<pos>&n;</pos>
+<misc>&rare;</misc>
+<gloss>someone who has come to share the good fortune of another</gloss>