I have seen exactly nobody ever route their brake hose external to the fork.
Read through this thread and you'll see it's about 50/50.
If you do a Google search for rockshox lyrik, you won't find a picture of the brake hose routed external, all of them internal.
This is pretty much true. All of them look awkward to me. Just because one guy does something one way and everyone follows doesn't make it the right way.
Because if you look at the rockshox guide you will see that is the opposite of what they suggest.
This is BS. I checked. It just says to "secure the disc brake hose into the guide". The guides on forks are different. Mine clearly directs the housing around the outside of the fork tube.
On the surface, and as a purist, one would say it should be routed internally so that it isn't exposed to the "elements" and because it's a naturally cleaner look. However, if you look at how closely it's routed to the fork there is little chance of something getting caught. I'd say I've got a much better chance of getting a cedar branch stuck in my eye. Also, every time I ride I get a stick tossed up into my spokes and kicked around. Having the cable routed internally increases the chances of that stick getting lodged and breaking a spoke.
In the end I've wasted way too much of my life on this subject.