The 2nd check is only since January 2021, you can still deposit the check. Do so ASAP.
The first check is older. You should try and deposit it.
The IRS sent the checks. You shouldn't claim on you didn't get them. Try to deposit them first.
So what happens if the check was lost? the IRS has a FAQ, this is pulled from the FAQ related to the first check:
Q F1. I received my payment by check, but it was lost, stolen or
destroyed. How do I get a new one? (updated March 22, 2021)
A1. If you received your payment by check and it was lost, stolen or
destroyed, you may need to request a payment trace so the IRS can
determine if your payment was cashed. See How do I request a payment
trace to track my first or second Economic Impact Payments?
If a trace is initiated and the IRS determines that the check wasn’t
cashed, the IRS will credit your account for that payment, but the IRS
cannot reissue your payment. Instead, you will need to claim the 2020
Recovery Rebate Credit on your 2020 tax return if eligible.
Note: If you are filing your 2020 tax return before your trace is
complete, do not include the payment amount on line 16 or 19 of the
2020 Recovery Rebate Credit Worksheet. If you do, you may receive a
notice saying your 2020 Recovery Rebate Credit was changed, but an
adjustment will be made after the trace is complete and it is
determined your payment has not been cashed. You will not need to take
any additional action to receive the credit.
If you do not request a trace on your payment, you may receive an
error when claiming the Recovery Rebate Credit on your 2020 tax
return. Since the payment was issued to you, you may not be eligible
for any credit.
If you were issued a payment and have not received it, see How do I
request a payment trace to track my first or second Economic Impact
The same page has a information on how to start a trace. It doesn't make it clear what you should do if you just haven't tried to cash the check. I don't think you would just claim you didn't get it, because the IRS computer knows it was sent, and would require a trace be done. This lack of trace could delay the rest of your tax return being processed.