Exporting is using a lot of resources. The file is not generated on the server but in your browser. For big models:

• Export using Collada (.dae). OBJ and STL requires a lot more power.
• Choose option: Group by Geometry
• Untick the LEGO logo checkbox
• Use Firefox (works way faster than Chrome for export)
• If you use chrome, make sure that you accept pop-up for Mecabricks. The last Chrome version is treating the generated file as a pop-up.

This is helpful. I was experiencing this same problem on some of the modular buildings.

Yes, thank you very much Scrubs. Totally forgot to reply, sorry for that.
I would have never ever thought that Firefox has better performance than Chrome, but in fact, it seemed to work better at least for this kind of task. What I did in the end, was, I removed everything except for one level and exported each level individually. Together with Firefox this worked. One just have to be patient. Firefox told me several times, that it detected some slowness, but one just has to click "continue" several times and at some point the download starts 😃

Thank you! Got the whole model and doing some renderings now 😃