Is Bigjigs Rail compatible with Ikea Lillabo?

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Yes:

All of Bigjigs Rail’s wooden train sets and wooden train track accessories are compatible with most other major wooden railway brands such as Brio, Thomas & Friends, IKEA, and more.

web.archive.org/web/20240607095508/https://www.bigjigstoys.co.uk/blogs/posts/everything-you-need-to-know-about-wooden-railway#:~:text=Which%20wooden%20train%20tracks%20are%20compatible