The figure is way out. Crossrail in London has a $20 billion total budget (£15b GBP), with 26 miles of tunnel[1]. But the tunnel is only part of the project, several billion is being spent on new regular track and station rebuilds, so the tunneling figure is really closer to $15 billion.
That's about $570 million per mile, but the Crossrail tunnels are just shy of 50% bigger in diameter than what Musk wants to build (20.5' vs 14'). And as the FAQ says, "reducing the diameter in half reduces tunneling costs by 3-4 times".
LA's tunnel might be costing $1B/mile, but how much of that cost is actual construction versus bureaucracy and mismanagement?
The closest thing is the Regional Connector project, which will be 1.9 miles of light rail and has a budget of $1.8B. But that's the entire project budget. Tunneling costs are only part of it; it's hard to find a finely grained budget, but total construction (including four new underground stations) is budgeted at $1.2B here [1], which is still "just" $600M/mile.
[1]: https://mtadash.mlmprojectservices.com/projects/5773#/cost
But that project was building a subway including station directly below a riverbed.