Is it ok for my boyfriend to go out to lunch with a girl I do not know?

there is this girl that came into my boyfriends work and at first was just bout car parts. recently she asked him to go clubbing with her and he had told her he was hanging out with me. she stated she didn't know he had a girlfriend and still invited me to go as well. and that they should have lunch soon. I told him I was uncomfortable with the situation because of what he's done in the past. (cheated and lied) lately things have been great and he's actually proving himself to me. but then she texted him and said they should go out to lunch this coming week and he said yes after he told me he knew I was uncomfortable. we had an argument over this. should I let him go and trust him this time around?
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+1 y
thank you all for your answers. I told him if its innocent then by all means go. I do have to start somewhere to give him a chance to gain his trust back. he basically told me he wasn't going to go because he doesn't want problems to escalate between us.
Is it ok for my boyfriend to go out to lunch with a girl I do not know?
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