The scholar carried out his lifework at the age of seventy.
- その学者は～を完成した is grammatically broken. その学者は～を完成させた is the correct one.
- We don’t usually say ライフワーク + 完成させる in this collocation although ライフワーク itself is a common loanword. ライフワーク is mostly used in such as “he is doing it as his lifework” (彼はライフワークとしてそれを手掛けている) or “that is his lifework” (あれは彼にとってライフワークだ).
Here is my alternative translation:
その学者は、一生の仕事 (or 生涯の事業) を70歳にして成し遂げた。（そのがくしゃは、いっしょうのしごと (or しょうがいのじぎょう) を70さいにしてなしとげた）
If his lifework is on a professional project (e.g. research on a disease) with his team, 事業 is better. If it is on a personal one or delivers a tangible output, 仕事 would be better. But they are mostly interchangeable.
I translated "at the age of 70) as 70歳にして, not 70歳で. Both are correct and sound natural, but the connotation of にして is “finally” at the age of 70. So, it’s a better collocation with one’s lifework.
成し遂げる literally means “to make it happen (成す) and it’s done/fulfilled (遂げる)”. So. 成し遂げる has the nuance of accomplishment through tireless hardworking.