Ports on my Older LACIE external hard drive are not compatible with new MacBook Pro

Apple has one. I am sure Best Buy sells one.

https://www.apple.com/shop/product/MJ1M2AM/A/usb-c-to-usb-adapter?fnode=ab6c1ba459c162b387ff878c2e98d0c03bf695da6be0e425fddeedb977cf2231ca85802cc71dcebecf17ea1e9810d575d75000cf96cadb38a3f7a68da634aa5b0bcc53004bcaa09616503d9d76f03e6eae471eea2809d59b6a6667afcdbbd22d

Firewire may e faster but did not see USBC-Firewire on Apple site.

You are correct. I have a OWC like that from years ago ... 2 Firewire and 1 micro USB-B (not a repeat on that "B"). You should have the cable from the original purchase ... I would think they gave you one. "Only at Apple stroe": https://www.apple.com/shop/product/HN8D2ZM/A/mophie-usb-c-cable-with-micro-b-connector?fnode=6a9f56af6794c92942a216a13189b11c5ab995f693a49664d382d05a74dbf3a63f612d28264b5a82b19452f2ec0b523f53c6e064c25e2b19692e990bb71e289581193717e242835003565503241a255202d3ad27789c8f433443cb746294489c

<< Firewire may be faster but did not see USBC-Firewire on Apple site. >>

The FireWire adapter available has a Thunderbolt-2 connector, so its use requires the US$50 ThunderBolt-3 <-> ThunderBolt-2 adapter. That extra expense in not justified if you can use USB cabling.

From your picture, it looks like you may have a USB-3.1 micro-B connector on that drive (upside down from this drawing):

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USB-3 is as fast as FireWire-800. For rotating magnetic drives, there is no speed advantage to FireWire-800.