Are you obligated to invite your good friend everywhere you go?

one of my good friends works in another place ten minutes away from me. we often have a similar lunch break time. but, sometimes my coworker wants to go out to lunch with just me (don't think she likes my friend that much).

but, my friend is the type who might be offended or annoyed if I don't invite her if she has lunch break too. but, sometimes I just want to be alone with my coworker so we can talk about work stuff and chat.

am I obligated to invite my friend all the time? she is the sensitive type but I feel caught in the middle.
Are you obligated to invite your good friend everywhere you go?
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