Do all real-time filters introduce phase lag, or can there be such a thing as "lag-less" or "zero lag" real time filters? Do all real-time filters introduce phase lag? I once heard of "lagless filters", but I don't think they can be used real-time (ie: on live data streaming in for a control system, for example, operating on incoming data), correct?

Obviously even though this question could be simply answered in a binary "yes/no" fashion, expounding upon the answer will be very helpful. 

Update: 

I just added some links in the comments below this question.

Also, here's some brief comments from a couple controls experts I know: 

Kenny Jensen:
"Forward-backward filters, aka smoothers, have no lag. You can't run them online though."

Ed Lim: "Hence they are not "real-time" filters. So I believe the answer is yes regarding real-time filters."
If a filter has any memory and that memory affects the current output, then that past data is lagged into the present.  If that filter is time invariant, then a memory of the present can potentially affect future output. e.g. is lagged into the future.  So, yes, unless the filter is memoryless or not time invariant.  

Note that a unit impulse at the origin is memoryless, but impossible to implement in any finite size system due to the speed of light being finite.