Trying to rewrite that sentence so it's comprehensible is an interesting exercise. How about this?
(I don't know anything about Vulkan, and there is some ambiguity in the quoted sentence, so I've given a few different versions with different meanings. Note that the ambiguity is not necessarily a flaw in the quoted sentence -- it may be perfectly unambiguous, albeit very unclear, to anyone with any knowledge of Vulkan.)
If a device is lost, the subresources of some images on other logical devices may have their layout become VK_IMAGE_LAYOUT_UNDEFINED. This happens if the VkDeviceMemory object to which the image is bound is associated with the same underlying memory resources as an external memory object on the lost device.
... or, if an image isn't necessarily bound to exactly one VkDeviceMemory object, ...
If a device is lost, the subresources of some images on other logical devices may have their layouts become VK_IMAGE_LAYOUT_UNDEFINED. This happens if the image is bound to a VkDeviceMemory object which is associated with the same underlying memory resources as an external memory object on the lost device.
... or, if it's the other logical device bound to a VkDeviceMemory object rather than the image:
If a device is lost, the subresources of images on other logical devices may have their layouts become VK_IMAGE_LAYOUT_UNDEFINED. This happens if the other device is bound to a VkDeviceMemory object which is associated with the same underlying memory resources as an external memory object on the lost device.
Or maybe a slightly different structure. "If a device is lost, and some VkDeviceMemory object is associated with hte same underlying memory resources as an external memory object on that lost device, then all subresources of any image bound to that VkDeviceMemory object have their layout set to VK_IMAGE_LAYOUT_UNDEFINED."
But I can't help thinking that this really wants a diagram. Nodes for the logical devices, the images, the VkDeviceMemory object, the "underlying memory resources", the external memory object. Labelled arrows for relationships like "bound to", "has as underlying memory resource", "is a subresource of", etc.
And it seems as if this business of "having your layout set to VK_IMAGE_LAYOUT_UNDEFINED" deserves a name. (Naming things is a powerful general technique for reducing cognitive stack overflows.)
"Under some circumstances, the memory resources associated with an image may be invalidated, in which case all subresources of the image will have layout VK_IMAGE_LAYOUT_INVALIDATED and [explain here the consequences of that]. In this case, the image is said to be layout-invalidated. " ... And then later, when talking about lost devices, you say "If a device is lost, images on other logical devices may be layout-invalidated. This happens when the image is bound to a VkDeviceMemory object, and that object is associated with the same underlying memory resources as an external memory object on the lost device."