My personal memory of LS3/5a's (20 years ago) is that they are very colored, in a beautiful way. They emphasize midrange and present it wonderfully. They are shy in the treble "air" and also they have a bump in the upper bass region to compensate for lack of lower bass.
This is kind of also a description of a 300B SET amp, or at least the typical one. Midrange emphasis with great beauty, lacking in air, great presence. Bass might be deep but lacking in control.
SO, on paper this is not a complementary match, but a match with similar biases.
BUT my own experience is that audio gear matching often achieves counter-intuitive results.
I would not have high expectations of this match but have no doubt it would be fun to try :)
And it might work well, quien sabe?