Train would require a change and there are no stations right near the base, but some close. Here is how I would determine the best route that works for your DIL, by working it backwards.
Go to Google Maps, type in RAF Lakenheath, then "search Nearby" for train stations and the flags will show all train stations in the area. For example, I did and saw that the town of Kennet just south of the base by about 5 to 10 miles has one, one called Lakenheath but north of the base, and a couple others nearby. Work with your family to find which one works best.
From there go to the National rail site ( http://www.nationalrail.co.uk/ ) enter in a departure station of London (All) and the station near the base that works the best. You will get a choice of departures, most all should be from Kings Cross Station.
Going back one step more, you need to get from Heathrow to Kings Cross, which the Piccadilly Underground line serving Heathrow will take you right there, and for the least cost.
I also saw in playing with Google that if you seek directions from Heathrow to Lakenheath and choose the public transit option, there are some buses listed that will get you very near there as well.