1. Lay low – meaning to keep quiet and not to attract attention to oneself; try not to be noticed，（刻意的） 保持低调; 也有（遇到麻烦时）低调行事, 避风头 以免招惹麻煩的意思。

Jason’s been laying low at work ever since he argued with his boss. 自从跟老板争吵后，jason上班时一直保持低调.

2. keep (one's) head down – 跟拉lay low 是一样的意思，To actively avoid conflict or attention; 低调行事; 避风头；

He's keeping his head down after being criticized for his offensive tweets.

在他攻击性推文而受到批评后，他一直保持低调。

3. Keep/manage/maintain a low profile - is another similar expression; 

avoid attracting attention to yourself; 不张扬；保持低调，, 不引人注目

He's been in a little trouble recently so he's trying to keep a low profile.

他最近有点麻烦，所以尽量不抛头露面。

4. “低调”还有一种表达方法是low key； 经常当作形容词用，低调、谦虚的; a low-key wedding 一场低调的婚礼。 

low key当副词用意思是「secretly， 偷偷地、稍微地，口语里很常用， 所以偷偷地暗恋别人可以说low key like/love someone；

I low key cheated on the test. 我考试偷偷作弊了。

5. high profile – attracting a lot of attention and interest from the public；  引人注目的，备受关注的；

high-profile public figures 备受关注的公众人物

high profile cases 备受关注的案例

6. fly under the radar - go unnoticed, especially for a long period of time; 指长期低调不被注意；

Back to the social media, I fly under the radar. I don't like anybody on Facebook. I don't want anybody to notice that I'm there.