You're right you will never be able to completely move on until you talk to her and tell her how you feel and ask her if she would ever consider giving your relationship another chance, the reason you haven't been able to move on is because you never had closure she said to you that she wanted to see what else is out there and not that she didn't want you and this is why you haven't been able to get her out of your mind because more or less you have some unfinished business. She never said she didn't want to meet she said that when you asked her to lunch it wasn't a good time maybe now that it is a new year and holiday hustle and bustle is over maybe you should try to contact her and ask if you could meet for lunch again or even just some quick coffee.
If anything you deserve to have closure so that you can truly move on knowing that you tried everything and can possibly find someone that is right for you and appreciates you, I don't think we ever forget our first or true love; there are people who after 50 years still remember that first true love. If she doesn't want you back then you will know that you need to move on without her in your life romantically and maybe you can continue to stay friends if you are able to do that without romantic feelings. It has been 3 years so she might have moved on without you or may be dating someone and didn't want to tell you or hurt you and if you talk to her you will know for certain and the only way you can do that is to meet her and see where her head is at. If she doesn't agree to meet you then maybe she is pretty much saying that she has moved on and doesn't even want to consider the thought of getting back together, if she turns down your offer to meet then ask why she will not meet you even for coffee and hopefully she will give an honest response and then you will know whether to pursue this relationship or to just let it go and move on and find someone that you can have a long lasting relationship with and who appreciate you and loves you unconditionally. Let me know if you have anything to add.
It could end the meeting if you do it as soon as you sit down what you should do if she agrees to the meeting is make small talk, ask how she is and what she has been up to things of that nature. It's pretty important to know if she is seeing someone before you meet that way you will know if the topic is even up for discussion. If she isn't seeing anyone I would bring up towards the end of the meeting but just don't wait until she is saying "Well I need to get going". This is something that is important for you to do in order for you to know exactly where you stand with her and if you have a chance at love again. Don't regret later in life never taking the chance to find out for sure and giving yourself closure if you don't do this now you will always wonder "what if" this way you will know and then you can make your decision about your future after that. If she says she still needs time then that is what you will have to give her so that she doesn't feel pressured into anything but 3 years is a long time to be apart and it is time for you both to make your decision so that there is no more wasted time.
Yes it could be up for discussion just get the time and place planned and then possibly ask her again is she doesn't answer your question again then take that at she is open to discuss things and when you meet be completely honest about your feelings and what you want from her, this way it won't be a guessing game and possibly her taking things the wrong way. This may be your only chance to truly tell her how you feel about her so don't let this chance get away. Remember to start out with small talk like "How have you been?" and "What have you been up to?" This way you will break the ice and make things more comfortable and remember this is not a stranger to you, you've dated her three and a half years so try not to be nervous this will show her that you really want this and are sure what you want. When you feel comfortable enough to say it tell her how much you have missed her in your life and see what her reaction on her face is. Ask her then if she hasn't answered your question in emails if she is currently dating someone and if so is it serious? After that take it from there with telling her how much you care about her and want her back. Keep a positive attitude! Good Luck to you.
Lunch will give you more time to build up the courage to tell her how you feel, if you go for coffee it won't give you that time you need to discuss everything you want to discuss with her. Make it a public Restaurant but some place where you can have privacy too. Give yourself about an half an hour before you start to talk about how you feel about her this would have given you enough time to get your food and start eating and you would have already had your small talk to lighten the mood. Make sure she has the time to stay longer than half an hour so that you will still have time to say everything you want to say to her. Good Luck to you!