When turning my handle bars, my bike produces a squeaking sound. I imagine it needs some oil somewhere. I am wondering, do I use the same lube I use on my chain, or something different? Where do I apply this lube?

Thanks.

If it squeaks, it's probably a case of dry,worn bearings. You'll have to disassemble the headset to get a proper look. You'll probably need to replace the ball bearings with new ones- the bearing cups are probably ok as long as they're not scored.

Bearing applications such as these require grease, not oil. I use white lithium grease on all bearings. Apply a generous amount to the bearing 'cup' and 'cone' surfaces when reassembling the headset. I spin the forks a few times before fully tightening everything up in order to spread the grease around the ball bearings.

Check your cable ferrules too. If dirt or corrosion gets in between the ferrule and braze-on, it will make a horrible sound when the bars are turned. Usually a grinding or creaking sound. High pitched squeaks are usually dry bearings.

When headsets squeak it might be more serious than just dry bearings which can be pretty quiet. The cause is often the skirts of headset cups rubbing on the corresponding cone, which indicated a bent steerer. Swing the bars back and forth and watch the gaps in the upper and lower headset units and see if there's any wobble. If so your steerer is bent.

BTW- All this assumes the headset is tight, because a loose headset also can squeak but that's simple enough to fix.