The .lay file extension is frequently found in files that are created in using the Apple DVD Studio Pro. DVD Studio Pro is a high-end software tool published by Apple. It allows users to produce DVD primaries that will serve as the master disk for software replication in software mass production process.
The .lay file stores layout information used to create the software specifically for optical disk storage. The .lay file format contains metadata internal to DVD Studio Pro and the DVD project and typically stored within the VIDEO_TS directory of a DVD project. It is also a proprietary file format of Apple and conversion to other file types or usage of such in other programs other than supported by Apple might not turn out successfully.
Please be noted that .lay files are just the layout of the project and not the project itself. It is the 'blueprint' of the project and not to be included in the projects when burning them to disk.
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If you have additional information about the LAY file format or software that uses files with the LAY suffix, please do get in touch - we would love hearing from you.