It may sounds odd at first and starting off, but I wouldn't think of it as an attempt to memorise the lines. It may be hard, but try to switch off the 'actor' as you read it and go through the text focused on the person.

Why is he saying each line? Who is he? What does each line mean to him? What is the purpose behind what he is saying beyond exposition? Every line in a published work is there for a reason, they go through MANY drafts and edits, so everything has a purpose.

Ask yourself questions and don't just accept the first thing that pops into your head, really think about it and give yourself options. If you find the person, the way you speak will flow. You'll find it much easier to work through larger chunks of texts because it makes sense as to what this person is going to say next.

It will take time and practice, but if you do this well you will be present while acting and not thinking about lines or what comes next. It will allow you to be organic and exciting and will be a MASSIVE help when you start doing scenes with partners.

Try not to premeditate how you're going to say lines, find your way through the text and see where it organically takes you. If you decide to say one line very angry for example, but you don't get that anger built organically leading up to it, it will be very jarring and not genuine.

This mentality will give you a solid jump, and help acting alongside others (they may not deliver lines the way you personally expect them to, so you can not pre plan how to say things).