Hi Jo,
Yup, some form of (spiked) flat platforms I've found are best, which are wide and deep enough to support the full dimensions of the Lockwoods. This is what I use and what you're looking for (should show on the middle of the screen):
https://www.google.co.uk/search?biw=...KGmv0Sl4ZsKIM:
And use them so that their widest parts are positioned horizontally, to successfully support the full width of your speakers.
If you can find a pair of Mana amp stands (for a Krell amplifier), such as the above, then those would be spot on, as they're both fully adjustable (you can raise or lower the boards, via use of the supplied spikes) in order to get the speakers bang on level [yes, this does make a difference to how they sound], also get the tweeters bang on ear height from your listening position, to achieve the desirable 'sweet spot', and provide the speakers with a nicely firm foundation from which to perform optimally.
Essentially what you're doing is replacing the floor in your room with a better 'floor' [one that is 100% level and rigid] for your speakers to sit on. This is especially critical (and sonically beneficial) if like me you're using the Lockies on an upstairs suspended wooden floor, although I know that doesn't apply in your case.
The difference this makes to tightening up the bass response, opening up the midrange, improving control of reproduced frequencies in all areas and allowing you to play music louder, and more comfortably (as the speakers will no longer 'sing along with the room' to the same extent) is significant!
If you can't find any such stands then it's a case of having something made to your spec at a local metal fabricator, who would build the outside spiked frames necessary, then it's simply a case of popping some (very) thick pieces of MDF board on top, levelling the whole shebang - and Bob's yer aunty...
If you need the dimensions, or any other info for the stands, just let me know
Marco.