Ask yourself three questions:
- Is he obligated to have lunch with you?
- Are you obligated to have lunch with him?
- Why are you worried this will make you look needy?
You want to know how to make someone socialize with you without seeming needy. Instead you should focus on creating healthy relationships at work rather than one-sided ones based on convenience.
When someone joins a new community, be it a workplace, a club, a sports team, a cafe full of regulars, or otherwise, people generally feel obliged to make that person feel welcome. One way people do that in an office is by asking you out to lunch when you have nobody else to ask because you're new, to let you meet some new people and feel like you are being included in the group.
Common courtesy goes both ways. If someone offers to hold a door for you, you should acknowledge that they did so (saying thanks, or smiling, or whatever -- not barging through the held door on your cell phone as if it is your God-given right to have people hold doors for you). If someone invites you to lunch, you should thank them, and extend the courtesy of not taking that invitation for granted.
Before you joined, your coworker was having lunch with other people (or alone). Perhaps they like spending the lunch break reading. Or chatting about sports. Or making connections with people in other departments to further their career. Or taking a nap.
Should he be obligated to have lunch with you every day and sacrifice his own time?
You say that he is the only person in your department. The same would apply to him, but he has found other people to have lunch with. Why is he the only person you can have lunch with? If you are working with other people from other departments, why not send them an e-mail or give them a call to ask them if they want to have lunch sometime?
If you don't have anyone you feel comfortable inviting to lunch, perhaps that is an indication that you should work on creating a better network of acquaintances at work. If you are depending on a single person to make you feel included socially, all you're doing is shifting the burden of create a social circle from you two the person you depend on. And there's no reason you should need to do that.
You recognize that you don't want to seem needy, yet your request is how to get the other person to accommodate your needs without offering anything in return.
When you were having lunch with your coworker, were you offering something of value in return? Were you providing interesting conversation, or just using him as a social crutch? Do you know what the person in HQ offers that you don't? Healthy relationships are not one-sided, and both sides offer something the other wants. Unless you can find something that you can offer the relationship, you will definitely seem needy.
To change that you need to:
- Stop depending on a single person for your social interaction
- Find more people who you can talk with to improve your happiness at work
- Work on finding ways to add value to the work relationships you have so they aren't one-sided