Most splitters introduce effectively un-noticeable lag. Only issue is when you split the feed into say an el gato and then back through as then that will introduce some lag.
a decent cheap splitter would be something like this
http://amzn.to/2l9wvOt
However if you are trying to feed through a capture card I would suggest getting a monitor with HDMI out to avoid lag. If that isn't the case then the above splitter should be perfectly fine.
