Thanks! Indeed it appears to be possible to apply a LUT to all clips in the timeline.
Actually how it works in my version (the latest 365) is:
as soon as I right-click the LUT, the selection of clips in the timeline is forgotten and the apply to all clips is done to ALL clips in the last selected track in the timeline.
To be clear: when I have say 7 clips in timeline 1 and 3 in timeline 2, and I select clip2 in track 1 and clip3 in track 2 (in that order), then
as soon as I right-click on the LUT, the selection is forgotten and the apply all will show that all LUTs in track 2 (the last track selected) will get the LUT, track 1 and the formally selected clips in track 1 are forgotten.
If the behavior if the right-click on the LUT is changed so that the selecteion of clips is not forgotten, then the apply to all clips (selected) would be ideal...
If not, then the text in the right-click menu should be changed into: Apply to all clips in the selected track.....
(I have forwarded this suggestion to CL.)