No Graviton EC2 instances in LAX Local Zone?

Based on the information available, it appears that you are correct in your observation that Graviton-based EC2 instances are not currently available in the Los Angeles (LAX) Local Zone.

AWS Local Zones are designed to bring select AWS services closer to end-users for applications that require single-digit millisecond latency. However, the availability of specific instance types can vary between different Local Zones and AWS Regions.

While Graviton instances offer significant benefits in terms of price performance and energy efficiency for various workloads, their availability is not uniform across all AWS infrastructure locations. Local Zones typically offer a subset of instance types compared to full AWS Regions, and it seems that Graviton instances are not part of the current offering in the LAX Local Zone.

It's worth noting that AWS continuously expands and updates its service offerings, so the availability of instance types in specific locations may change over time. If Graviton instances are crucial for your workload in the LAX area, you might want to consider using the nearest full AWS Region that supports Graviton instances or contact AWS support for the most up-to-date information and potential alternatives.
Sources
Not able to create t4g.small ec2 type instance in mumbai local zone | AWS re:Post
Use Graviton instances and containers - AWS Prescriptive Guidance