The bullet diameters of 7.62x54R and .303 are similar, as are the bore diameters. .303 tends to be a bit larger. The .303 case is longer that the Russian. The barrel can be rechambered, although fired cases will look rather odd. If the barrel were set back, fired cases would be normal. I have no idea if the 7.62 will work through the magazine. Bolt would be fine, extractor might need adjustment.
The conversions have been done to take advantage of really cheap 7.62 ammunition. Whether it makes sense, or is cost effective is an open question. It will certainly lower the value of any decent Lee Enfield.