As was said, if you did not crop the original image then you have an aspect ratio out of the camera that will "match" your desire for a 24x36 print.
That being the case, the "simplest" approach would be to just use the Lightroom Export function. The questions will be:
1) How does the driver handle files that have a ppi resolution "tag" of various values? The driver may or may not "care" -- Lightroom by default sets a value of something like 240 or 250 ppi (you can change this). For many printer drivers this tag doesn't matter as long as you don't resize to a specific dimension in inches at a given ppi/resolution. You'll want to find out for the specific printer (maybe run a test if you can't find info in the printer docs)
2) How does the printer/driver handle files/images that don't "match" the print size you want? In other words, if you send a file and tell the printer to print at 24x36 and the actual/original image has a resolution that would produce that image at, say, 200 ppi (which would be a pixel resolution of 4800x7200 pixels) would the printer properly handle that job, by resampling the image to a proper resolution internally (most digital printers can do this)? If it can handle it, then for your purposes you may be happy to let the print driver do its job. However, if you have any doubt about this, then you can, in the LR Export dialog, tell LR to Resize/resample the image to a specific print size and a specific resolution. So for example for your job, specifying 24x36 Inches at 300 ppi will produce a resized image file that would meet the common "standard" for print resolution.
3) Then, the HP Export dialog has settings for "output sharpening" where you can specify both a "target" and an amount. For printing, you can choose either Matte or Glossy paper as a "target" and then an amount. There is a difference in how Matte and Glossy "targets" are rendered. I'd advise you to run some small test prints to get a look and feel of different settings between doing a "final" big print. Another thing that has come up here is that for the Lightroom output sharpening for a print, the ppi tag does matter. It has been "reported" that the developers set print sharpening (using a higher ppi "value") differently than sharpening for screen (a lower ppi "value"). Because of this, it has been advised that if you are preparing specifically for print that you ensure that your ppi "tag" is at a relatively high value. I'm not sure of what the "lower" bound is, maybe someone who knows can chip in...?
4) The last thing I'll chime in with is whether you want "full control" of all this, by doing your own resizing of the image and then "tweaking" the results yourself. If so, the best option could be to Edit in Photoshop, use the Image Size dialog where you can set the size in inches and the resolution/ppi to say 300 ppi and specify in the dialog that PS should resample the image to that size/resolution. Then, you can take the final image and do things like output sharpening. You can do this in PS using one of the "fancy tools", or just Save (and Close) the image so that you can work on the saved copy in Lightroom (it will automatically show up in your library/catalog)
If all of this is "over your head", then you should stop and "read up" on digital printing! Look in the FAQ "sticky" at the top of the section "page" here and also check out the "Beginners' Guide" sticky:
Hope this helps a bit!