"Let's" is a great way to suggest an action to a group of people, especially friends. In this sentence, it is implied that longest means "the longest amount of time" so you don't need to say all of that. I hope that this helps. :)
複数の人（特に友達）に何かを提案するなら、"Let's" はピッタリの表現です。
この文では、"longest" が "the longest amount of time"（最も長い時間）を指すことは文脈で伝わります。ですから、"the longest amount of time" と全て言う必要はありません。
Let's have some fun! Let's compete to see who can stay in the sauna the longest!
I challenge you to see who can stay in the sauna the longest!
Let's see who can stay in the sauna the longest!
Using this sentence is daring your friends.
"dare" who has the courage or who is brave enough to do something.
Let's have some fun! Let's compete to see who can stay in the sauna the longest!
"compete" to have a competition
I challenge you to see who can stay in the sauna the longest!
"challenge" to ask someone to participate in an action
Let's see who can stay in the sauna the longest!（誰が一番長くサウナにいられるか競争しよう）
ここでは相手／友達を "dare" しています。
"dare" =〔人を〕挑発する／〔人に〕挑む
Let's have some fun! Let's compete to see who can stay in the sauna the longest!（ちょっと遊ぼう。誰が一番長くサウナにいられるか競争しよう）
"compete" = 競争する
I challenge you to see who can stay in the sauna the longest!（誰が一番長くサウナにいられるか競争しよう）
"challenge" = あることに参加してくださいと頼む
phrases used often in a competition context, implying or starting the competition.
"Let's see who lasts" is a very short way of initiating such a competition.
どちらも、人と競争をするときによく使われるフレーズです。
"Let's see who lasts"（誰が最後までいられるか競争しよう）は、このような競争をスタートさせる非常に簡潔な言い方です。
Let's see who can remain in the sauna the longest!
Let's see who lasts the longest in the sauna!
Let's see who can remain in the sauna the longest!
In these sentences "See" is used to talk about an experience you will witness. You will be there to watch or see who comes out of the Sauna last.
Last / remain - to stay inside the sauna
I will not last another winter.
Tom will remain in Canada until spring.
Longest - for the biggest period of time.
This is the longest road in the country.
Let's see who lasts the longest in the sauna!（誰がサウナに一番長くいられるか競争しよう）
Let's see who can remain in the sauna the longest!（誰がサウナに一番長くいられるか競争しよう）
これらの文では、"See" を使って成り行きを見守ることを表しています。そこにいて誰が最後までサウナにいられるか見届けるということです。
Last / remain - サウナの中にいる
I will not last another winter.（私は次の冬は越せないだろう）
Tom will remain in Canada until spring.（トムは春までカナダにいます）
Longest - 最も長い時間
This is the longest road in the country.（これは国内最長の道です）
Let's have a competition to see who can stay in the sauna the longest!
This highlights the competition and the goal
Let's have a competition to see who can stay in the sauna the longest
Or let's see who can last the longest!
これは競争と目標を表します。
"Let's have a competition to see who can stay in the sauna the longest"（誰が一番長くサウナにいられるか競争しよう）
または、"Let's see who can last the longest!"（誰が一番長くいられるか競争しよう）
Let's see who can stay inside the sauna the longest!
I bet I can stay in the sauna longer than you.
When in the sauna with friends, you want to say something like "Let's have a competition to see who can stay in the sauna the longest". Either of the above comments should fit that scenario. The function of both the example sentences is to challenge someone to do something.
友達とサウナに入っているときに、"Let's have a competition to see who can stay in the sauna the longest"（誰が一番長くサウナに入っていられるか競争しよう）のようなことを言いたいということですね。上記どちらの文も使うことができます。
どちらも相手に挑戦を挑むときの言い方です。
Let's have a competition to see who can stay in the sauna the longest
I challenge you to see who can stay in the sauna the longest
When you are with friends you want to enjoy yourself and have some fun so you might play games/competitions these can also be called 'challenges' you challenge someone to do something
Sauna are very hot and some people can't take the heat for too long so you might want to see how long they can last and have a bit of fun as well
友達といると、一緒にゲームをしたり競争をすることがあるかもしれません。これは 'challenges' といいます。
※ challenge someone to do something =（人）に挑戦を挑む
サウナは暑くてなかなか長く入っていられませんから、どのくらい我慢できるか競争すると面白いかもしれません。
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