zip compression is lossless, so you will not loose anything.
All you will loose is application compatibility - not all applications supports zip compressed tiffs.
It's up to you to decide whether you are using such applications and does it worth it.
Do you see any value to enlarging the file when exporting to tiff.
What do you mean by "enlarging"?
Increasing resolution? No - I don't see the point to do this if you don't need to.
Increasing file size? It depends. If you are using apps that don't support compressed tiffs and want to process your images in them then this is the only way to go. Otherwise don't see the point either.
You won't lose any scalability when you use compression. the application that will work with the tiff will unpack the compressed file, scale it up, then packet again. The resulting zip file will of course be larger than the original zip. Any loss of quality will be due to interpolation of scaling.
Whether you enlarge via Lightroom on export or Photoshop, interpolation will occur. The result of acceptability is subjective and often affected by the content of the image.
The size you can print is restricted by the amount of pixels you have divided by the print resolution. Many large format printers will work just fine with an image that is 200ppi. Yielding a larger image than if it were 300ppi.
In addition I would question whether you need to be exporting 16bit files for the print. Technically, yes, it has better quality than an 8bit file but in many real world examples I have yet to find anyone who can tell the difference.
Discuss with the printer service their requirements and perhaps ask for tests at different resolutions (300/240/200/180) and different bit depth (8/16)