I cancelled the lesson because I wasn't sure if I could make it in time.
間に合う というのは
make it で表すことができます。
I cancelled the lesson because I wasn't sure if I could make it in time.
直訳すると「その（レッスン）時間までに間に合うかわからなかった（確実じゃなかった）ので、レッスンをキャンセルした」
となります。
make it in time は「時間に間に合う」という決まり文句です。
ご参考になれば幸いです。
I canceled the lesson because I was not sure if I could make it.
間に合うか分からなかったのでレッスンをキャンセルしました。
make it には、「間に合う」という意味があり、よくcanと一緒に使われます。
例
時間通りにいける？
Can you make it on time?
間に合うか分からないなぁ
I am not sure if I can make it.
I cancelled the lesson because I didn't think that I would be able to make it on time.
In this case, "make it" means arrive. You use "would" in the second part of the sentence because you are unsure about if you could make it or not. I hope that this helps. :)
I wasn't sure I could make my lesson so I canceled.
I got stuck at work so I canceled my lesson.
I wans't sure I could get away from work so I canceled my lesson.
In the context of the first sentece, to "make" a lesson is to arrive on time. This sentence is a very natural way to say that you weren't sure you would arrive on time so you canceled.
If you get stuck at work, it means that you cannot leave when you thought you could. For example "I'm sorry I'm late, I got stuck at work."
To "get away" is to escape or to leave. To "get away from work" is to leave work in a timely manner.
一つ目の文の "make" は「間に合う」という意味です。この文は、間に合うか分からなかったのでキャンセルしたと伝える非常に自然な言い方です。
"got stuck at work" は、仕事が手間取ったという意味です。
例えば：
"I'm sorry I'm late, I got stuck at work."（遅れてごめんなさい、仕事が手間取ってしまいました）
"get away" は「逃げる」「離れる」という意味です。"get away from work" は、タイミング良く職場を離れることを表します。
It was looking like I wasn't going to make it on time, so I cancelled.
I cancelled the lesson because I got held up at work and wasn't sure when I'd be free.
"It was looking like I wasn't going to make it on time, so I cancelled." - A great way to say that an outcome looked likely is by saying "it was looking like...." and "make it on time" is a common way to say that you were going to be late.
"I cancelled the lesson because I got held up at work and wasn't sure when I'd be free."
- to be "held up" is a common way to say "delayed" or "slowed down" and is used when referring to not being on time. When you are no longer "held up", you are then "free", so that is why you could complete the saying with "be free".
"It was looking like I wasn't going to make it on time, so I cancelled."（間に合いそうになかったのでキャンセルしました）
- ある結果が起こりそうだったことは、"it was looking like...." で表せます。"make it on time"（間に合う）は遅れそうだったことを伝えるときの一般的な言い方です。
"I cancelled the lesson because I got held up at work and wasn't sure when I'd be free."（仕事に手間取っていつ終わるか分からなかったのでレッスンをキャンセルしました）
- "held up" は "delayed" や "slowed down" の一般的な言い方で、間に合わないことを表すときに使われます。"held up" の状態が解かれると今度は "free"（解放された）になります。文末にある "be free" はそういうことです。
Please accept mu apologies, I need to cancel because I don't think I can make it on time.
Im sad to say I have cancelled my lesson as it is unlikely I can get away from work on time.
Please accept mu apologies, I am cancelling my lesson because I don't think I can make it on time.
Offering an apology or saying something like :"Im sad to say" shows the person that you respect their efforts and indicates that there is a serious reason you cancelled. It is polite to apologise for a cancellation and then explain the reason you are cancelling.
謝罪をしたり、あるいは "I'm sad to say"（残念なことに）などと言うと、相手の努力に対して敬意を表すことができ、また、大事な理由があってキャンセルをしたというニュアンスになります。
キャンセルしたことを謝ってそれからその理由を説明すると丁寧です。
I blew the lesson out because I had doubts about being able to start on time
When talking about an online English lesson which you cancelled because you were not sure if you could make the lesson on time, and you want to explain that point, then you can use the abovementioned suggestion.
To blow something out = to abandon a person, idea or project.
時間に間に合うかどうか分からなかったので英語のオンラインレッスンをキャンセルしたなら、それは上記のように説明できます。
To blow soemthing out = 〔人を〕見捨てる／〔考え・計画を〕断念する
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