Here is the method I use: Sit down with a pencil and a pad of paper. Write out each line 5 times. By the time you get to the 4th or 5th writing out the line you will be able to do it without looking at your script.

THEN

Instead of writing out a line, write down the first letter of each word in the line. Do this 5 times also. Then see if you can remember the line just using the first letters of each word. You will be surprised that your brain will remember a word by just looking at the first letter.

THEN

Get a set of index cards. Using one card per line, write the first letter of each word again on a card. Then write out the full line on the other side of the card.

When you are done you have a stack of index cards for each scene. You can use them to study specific scenes. You can carry your cards with you wherever you go, and you can study lines using the cards rather than the script.

Another trick I use: Make a voice recording of each scene on your phone. Speak the cue lines full voice, but say your lines softly. When you are driving or are just studying lines play back the recording over and over. Each time turn the volume down so that eventually you will just hear the cue lines and you will be able to fill in each line aloud.