Thank you for the early lesson. でも十分伝わったと思いますが、細かく言えば the early lesson だけだと「朝早い」という意味なのか「時期が早い」という意味なのか曖昧になってしまいそうですね。質問文にも書かれているように「レッスンを早めに始めてくれて」という部分を表現するのがいいかと思います。
Thank you for starting the lesson early (for me).
（私のために）レッスンを早めに始めてくれてありがとう。
I appreciate that you started the lesson earlier for me.
◆Thank you for starting the lesson earlier.
レッスンを（いつもより）早くはじめてくれてありがとう！
→シンプルですが、"Thank you for 〜ing" は何にでも幅広く使えるので
覚えておくのがオススメです！！
◆I appreciate that you started the lesson earlier for me.
私のためにレッスンを早めにはじめてくださり感謝しています。
→こちらは少し固めな表現。先生との人間関係ある程度あってカジュアルなほうが
気持ちが伝わりやすい場合もあるので、距離感で選んでください！
It is so good of you to start the lesson earlier for me, Thank you so much.
Thank you so much for the extra time that you are giving me.
>▪It is so good of you to start the lesson earlier for me, Thank you so much.
>This sentence is saying to the teacher that he/she is very kind and helpful to start the lesson earlier.
.........................................
>▪Thank you so much for the extra time that you are giving me.
>This is a simple way of thanking the teacher for the extra minutes added to the lesson.
............................................
>▪It is so good of you to start the lesson earlier for me, Thank you so much.
訳：予定より早めにレッスンを始めて下さってありがとうございます。
>これは予定より早めにレッスンを始めてくれてありがたく思っていることを伝えることができます。
>▪Thank you so much for the extra time that you are giving me.
訳：予定より多く時間を下さりありがとうございます。
>予定より多く時間をもらったことをありがたく思っていることを伝えることができます。
Thank you for thinking of me and being considerate.
I appreciate you taking time out of your schedule to take the lesson early.
You should thank your teacher profusely, because starting the lesson is a great courtesy. You have a good teacher. You can simply tell him/her how appreciative you are that the lesson was started earlier to accommodate you.
I really appreciate your kicking off a little earlier
Thanks so much..' is a great way to offer your heart-felt thanks to someone. Similarly, but slightly more reserved is: "I really appreciate...."
To kick off = apart from a game of football or team game involving kicking a ball to start the game, this verb has a wider meaning and may be applied when anything starts: for example, the working day, a concert, a holiday etc
"My holiday kicks off on the third of July!"
Thanks so much..'は、誰かに感謝するときに使う素晴らしい表現です。
よく似ていて、やや控えめな表現が "I really appreciate...."「～に感謝しています」というフレーズです。
To kick off = フットボールで試合を始めるときにボールを蹴るという意味ですが、これは色々な意味がありますが、この場合、例えば仕事、コンサート、休暇など何かを始めるという意味です。
"My holiday kicks off on the third of July!"
休暇が7月3日に始まる！
Thanks for starting the lesson a little earlier today
I appreciate you starting the lesson earlier for me
If you say thanks to someone then you are telling them you are thankful you can also way you 'appreciate' them doing it for you
earlier means to start something a bit of time before or in advance
"It is really kind for you to start the lesson earlier for me, thank you"
In order to express that you are grateful for the teacher starting the lesson three minutes early for you, you can state "It is really kind for you to start the lesson earlier for me, thank you". This lets the student know that you are aware of the kindness they have showed and appreciate it.
レッスンを3分早く始めてくれたことを先生に感謝したいなら、次にように言えます。
"It is really kind for you to start the lesson earlier for me, thank you".
（レッスンを早めに始めていただきどうもありがとうございます）
このように言えば、先生の親切に対して感謝していることが伝わります。
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