Hi, I hope I can offer some help with your question.
From the situation you have described, you split up during a period of stress when your girlfriend was going through a bereavement and at the same time you lied about money to her.
It sounds like this has damaged her trust in you, and so at the moment it is important that your focus is on rebuilding that trust. This will involve talking through why you lied to her so that she can understand your thought process in this and determine whether she feels confident that due to the repercussions from this, you would not be inclined to lie to her again in the future.
I wonder if she means she needs time to rebuild this trust in you to hopefully get back to where you were together before this happened, or that she needs time away from you.
It sounds like she is enjoying meeting up with you but needs time to rebuild this trust. This will simply take time and patience, and consistency on your part.
The trust has been broken in some ways due to a lack of respect of her, and therefore it is this respect that needs to be worked on - to respect her perspective and her feelings, so that you are avoiding only considering your own feelings and what you want from the relationship, but also considering hers.