Can I lace a 36 hole hub to 48 hole rim? I'm trying to install a 3 speed, 36 spoke hub into my 48 spoke rim.

I want to try and retain the larger wheel if possible instead of downsizing to a 29" tire. I'm getting mixed information that it will or will not work. 

Can you help me in any way? I read where someone was lacing 12 spokes in a radial set up but the lacing and location of the remaining spokes was very misleading.

Is this possible?
You do not want radial spoke pattern on a rear wheel - that's not good for power transmission or for braking.

You have two options.


Lace the wheel three-cross like normal, but leave every 4th hole empty.  Downside is this will give a terrible lacing pattern, and you may need to buy a mix of longer and shorter spokes to do it half-decent.  Simply threadding the nipples on further or less, may work for some spokes, but there will be insufficient thread engagement on some spokes.  

Surprisingly, a set of spokes costs more than a rim, so there's no cost saving.

And this will build a wheel that is not as strong as a properly spaced 36 spoke rim.
Buy the right rim and do it properly.  A 36 hole rim would be much better, and will only use two lengths of spoke (longer on left, slightly shorter on the right.)


Your suggestion of radial might have been related to a "half radial" lacing pattern like this one:

  

However notice that there are still the same number of spokes to holes.  The 18 spokes on the left side will be shorter so you have to buy 18 shorter spokes.  It looks like this fully done:



Notice the spokes are laid out evenly spaced still?

Further info here  http://www.sheldonbrown.com/wheelbuild.html#half-radial

Finally you might have been thinking about properly engineered racing wheels like this one:


These have been properly engineered to work with 2 spokes from the drive side and one on the non-drive side (left side)  You can't get the same effect by simply missing out spoke holes.