I have registered for the Milano Marathon two weeks later and did Rome Marathon in 2014 so I am somewhat familiar with the regulations for Italian races. There are two ways for foreigners to be allowed to start and that is either to get hold of a medical certificate signed and stamped by a doctor or to be a member of a club recognized by your national athletics federation. As it is usually cheaper and easier to become a member of a club I recommend you to go that way.
Edit: You can also buy your own stamp and be "creative" with the medical form. I know this is quite common for races in Italy and France.
I don´t know about this specific race but I have done the Rome Marathon in 2014 and have signed up for the Milano Marathon this spring. It is correct that you either need a medical certificate OR a membership in a club connected to your national athletics federation to race longer than 20 km in Italy.
If the Welsh Athletics is a member of the IAAF you should be fine by providing a copy of your membership card when signing up for the race. But your girlfriend will need to either become a member of a club or get a medical certificate signed and stamped by a doctor. I would recommend her to join a club as this is usually cheaper and easier.
Also,expect the registration and verification progress to be slow after signing up. The organizers usually manually check all documents and this can take weeks.
The FAQ on the VLM website says that the results are out from the 10th of october:
Q. When do I find out if I have secured a place through the ballot? A. The earliest date you will hear from us is Monday 10 October and all applicants should have heard the outcome by Monday 17 October. Everyone from the UK who gains a place in the ballot is sent the Congratulations magazine. A random selection of approximately half of unsuccessful applicants will be sent the Commiserations magazine and the remainder will be sent an e-zine version. Overseas applicants will be contacted via email.
Open the race fast to bank in time for the second half will most likely end in disaster. For a beginner I think the best tactic is to run in an even pace, althought many say a slightly faster second half (negative split) is preferable.