LinkedHashMap<IndexNode, IndexNode> ZipFileSystem.inodes contains only non-null values.

            if (inodes.containsKey(lookup)) {
                parent = inodes.get(lookup);
                node.sibling = parent.child;
                parent.child = node;
                break;
            }

It means instead of separate containsKey+get calls, we can use single LinkedHashMap.get call and then compare result with null.
Result code is a bit simpler and faster.

            parent = inodes.get(lookup);
            if (parent != null) {
                node.sibling = parent.child;
                parent.child = node;
                break;
            }