In days past this would be closed as a dup of bug 464231. But libcal.js is in the future. However, to expand one what Richard said, even if both OS are using the same version of TB (which will be rare I think) and same version of lightning, cross platform profile sharing isn't officially supported at the Thunderbird level. So I don't see how this can be officially supported or be a useful goal for Calendar. But I could be wrong.
Bug 1348924 Comment 5 Edit History
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In days past this would be closed as a dup of bug 464231. But libcal.js is in the future. However, to expand on what Richard said, even if both OS are using the same version of TB (which will be rare I think) and same version of lightning, cross platform profile sharing isn't officially supported at the Thunderbird level. So I don't see how this can be officially supported or be a useful goal for Calendar. But I could be wrong.