You can absolutely go out to lunch with them!! I am in a similar situation, as I have posted above (see my post on work emails)..I guess its a matter of boundaries, and allowing yourself to get to know them but at the same time making sure that you are no absorbing the bad stuff. The majority of people i work with are not christians, and there are on occasion some profanity thrown around the office, especially in my job as it is very stressful. In addition the content of what I am dealing with is nearly always explicit, dealing with pretty heavy stuff that involves swearing (and yes we do actually have to write the swearing in our reports, just as it was told to us) as well as topics such as abortion, sexual abuse, verbal abuse, neglect, and other issues.
An incredibly wise woman who I consider a bit of a mentor of mind told me a remarkable thing that I am endeavouring to do everyday....at the end of the day, when i jump in my car and im on my way home, I pray to God to wipe my mind clean of all that I have seen and heard. Apparently christian counsellors are taught to do this when they're studying, because you hear the worst of the worst and there has to be a way of not letting it sink into your spirit. I love this idea, of God being able to make you forget all those things you should forget, and in this way I am finding I am not getting bogged down in the bad stuff, and retaining all the info I need to continue the next day without it affecting my spirit or my relationship with God.
In addition, I would say that going out socially with these people is a great way for you to not just relate to them, but for you to SHOW that you're different. For one thing, you dont drink, so go out with them and NOT drink. Show them you can still have a good time. Being a christian shouldnt mean that you miss out fellowshipping with these people just because you dont do everything they do! Now, dont get me wrong, if they're participating in something immoral or illegal do NOT do it too....but going out to dinner, having lunch, even going out on a Friday afternoon and having a coke (or a diet coke whatever u fancy) while they drink is totally ok in my opinion. You have to keep to what YOU know to be right, and what you feel will keep your relationship with God and your testimony to your workmates safe. I have known many people who have been turned to Jesus purely because they watched their friends who were Christian having a good time WITHOUT alcohol, and realised that it was possible!!! Don't be afraid to read your bible at work on your breaks, or to comfort a workmate going through a hard time with something that is slightly biblical in theme. I have made it a point to find out what each of my team members likes (whether it be potato chips, a particular drink, a chocolate bar) and I have started buying that thing for one workmate a week...costs me next to nothing, but it shows I care and I noticed...couple that with their knowledge already that I am a christian and suddenly you have a positive experience with a christian going on! Very cool! Dont make it a secret that you're a christian, and you will find that so long as you dont shove your faith down people's throats they will respect you for it. Most important of all, be yourself, and be ready to answer whenever someone asks you why you are the way you are, be ready to share your faith with them IF they ask. In the meantime, just love them. You never know, you just might be the person Jesus has been waiting to place with these people to show them there is a better way!!!!
Bless you! xox