Gibson Sonomatics (set E340) were gauged: 13 / 17 / 26(w) / 56 / 46 / 56. The Shadows had a promo/endorsement deal with Selmer from the mid-sixties onward and used/recommended that set of strings, whether on the acoustic Gibsons they were then using or on their various electrics.
At the latter end of the 1960s, Gibson introduced a lighter version, Sonomatic Light Gauge (E340L), which were sized 11 / 12 / 19(w) / 32 / 42 / 52.
During his solo years, Hank was using E340s on one Burns Marvin and either E340Ls or Fender Rock'n'Roll (which were a fair bit lighter) on the other.
E340Ls were notable for their
very light second string (12), which was even lighter than the second in an Ernie Ball Slinky set (13).
If the current L5 set is gauged 11-52 (and it seems to be 11 / 14 / 19(w) / 30 / 41 / 52), the gauge seems to be related rather more to the E340Ls rather than the pukka E340s. But only three out of the six strings are the same gauge and of the other three, one is heavier (the B) whilst the D and A are lighter.
Incidentally, the L5 strings are available in the UK:
http://www.stringsdirect.co.uk/products/698-gibson_l_5_pure_nickel_wound_jazz_electric_guitar_stringsJN