I'm very sorry. Something suddenly came up, so I couldn't attend the lesson.
I apologize for missing the lesson. Something suddenly came up.
ご質問ありがとうございます。
日本語と違って、英語にするとこの文を二つに分けるのが自然です。文化的に最初に謝り言葉を言います。そして、説明を挙げます。
謝り例文:
I'm very sorry.
I apologize for missing the lesson.
I'm sorry that I couldn't attend the lesson.
Please forgive me for not attending the lesson.
説明例:
Something suddenly came up.
There was something that I had to take care of.
ご参考になれば幸いです。