Como dizer "dar uma lida" em inglês

*Adding:

to run over = dar uma lida rápida, passar o olho

→Example:
Run over Lesson 2 once more.

*Adding:

to run down = dar uma passada rápida de olho

→Example:
Please run down the Safety Plan once more before we hand it in.

FONTE

*Adding:

to go over = dar uma revisada, examinar pra saber se contém erros

→Example:
Do you usually go over your notes before class?

Opção:

Have a read (BrE):

I was having a quiet read when the phone rang. - Oxford

Another way:

Take a brief look

Let's take a brief look at two of the most popular words in English.

Uma interpretação:

Por favor, dá uma lida nesse email antes de eu mandar. = Please, look over this email before I send it.

Eu dei uma lida rápida no jornal. = I looked over the newspaper. / I gave the newspaper a quick read / a quick scan.

I would say: to skim
I'll skim the newspaper.

from thefreedictionary

read up
To study or learn by reading: Read up on the places you plan to visit before you travel.

Do you see the difference? When you read up on something, you are trying to learn about something and are possibly using several books in your studying.

To skim, to scan, etc. are all distantly related to "reading up", but they are still far from the meaning.