My impression was that once you have generated the atom coordinates in VMD, you would use Axel's topotools to create the LAMMPS data file and input script with the force field parameters. Since you choose these force field parameters manually, they could be either TIP3P or SPC/E, or anything else you desire.
Alternatively you could save the coordinated as an .XYZ or .PDB file and load them into moltemplate and then choose SPC/E or TIP3P water. Those water models are already included with moltemplate, so you don't have to specify the parameters manually. There's an example/tutorial how to do this included with moltemplate. Currently, you can also get the files for that example here:
(The URL for these files could change in the future.)
This exact topic is also discussed in chapter 4 of the moltemplate manual. This is the main introductory chapter, and it is only a few pages long.
I hope this gets you started.