Cross-Region Load balancer, only supports public Load Balancers.
I would recommend using Azure Application Gateway, you can use this internally, and as long as the Application Gateway has visibility into the second region (i.e. peered VNET) you can specify it as a backend.
Keep in mind that Application Gateway is a regional service though, so if the region goes down, the Application Gateway may fail.
- Reference: Decision tree for load balancing in Azure
If you need something more globally available, then you could utilise Azure Front Door, and only allow traffic from your company's IP address.
Refer: Configure an IP restriction rule with a WAF for Azure Front Door