The chain(s) provided by LE generally do not contain root certificates (they're already included in the clients trust store and should never be sent by TLS servers). The current default chain does not include DST Root CA X3 itself (though it contains a certificate with this issuer).
But yes, you can request a chain from LE that does not include the final cross-sign up to DST Root CA X3. This is called the alternate chain. This chain must be explicitly requested by your ACME client - how to do this depends on your client, often it's a command line argument called preferred-chain (or similar).
There is no explicit time-frame, but you can expect this chain to stay for some years, possibly until late 2024. The chain leading to the expired root is supposed to help with compatibility for some clients (mainly Android), so it's going to stay with us for a while. We're aware that some clients don't like the current default chain, which is why the alternate chain is available
The current and alternate chain served, as well as any upcoming planned changes can be found here: