Is this possible to make a module with both castellations and LGA?
Thank you for posting this question.
Mechanically, there is nothing that will stop you from using both assembly methods, as long as the receiving PCB, to which you assemble the module caters for this. What I mean here is that you can make a receiving PCB with either method, or even both, but you will have to remember that if you use castellated pads and not LGA, you will still have the LGA pads exposed under the module, and therefore you will risk shorts if you have any copper exposed on the receiving board, for example vias.

Electrically, you will have to keep in mind that you will be adding a stub to all the lines you bring out, which means that the integrity of hi-speed signals will be compromised. 

There is nothing stopping you from mixing the two technologies.

One thing that is worth mentioning, is that to use LGA pads, you will have to have a controlled assembly process, which will use solder paste masks and some form of solder reflow. Castellated pads are easier to hand assemble, even by an untrained user, and is easier to inspect, however, it can cost a little bit more to manufacture.