You have to proceed at a comfortable pace so you can feel secure with each step. However, she did more harm by showing she will lie to you (or herself) in the porocess. She needs to back off and really decide how she is going to handle herself. Relationships have to be based on communication and honesty. She is failing at both of these for now. (You may be guilty of stuff, but I can only go on what you have said so far.)
As for the first date being appropriate for oral sex or just a kiss, that is something that should be communicated up front. A lot of polyamory is realizing that your assumptions are not necessarily other people's assumptions. So you need to be able to clarify it. For example, talk about what you are comfortable with. She can say shwt she would like to do. Talk through some possible situations. Make it so that honesty is the best decision she can go with.
i wish you well.