You can have multiple 'A' records for a domain name that point at different IPs.

However, DNS doesn't do application health checks, so if your server or application goes offline, requests will still be sent to the unreachable server. Reachability can be solved with dynamic DNS, short TTLs and aggressive health checking. For example, DoIT could provide a dns server zone that allows dynamic updates but it would the application specialist's problem to write the health checker and DNS update scripts.

DNS also doesn't keep state, which can be important for maintaining some tcp based interactions. Dynamic DNS doesn't solve this problem.

Given the above, load balancing with static DNS is generally recommended against unless the application itself can be made to handle failover. Other load balancing techniques should be investigated.