My client received Form 1444 in May, 2020 stating she would receive a impact payment of $472.40. She never received it. Is there a way to add that amount into her LaCerte Form 1040 for the 2020 tax return?

Is she really sure she didn't receive it? For example by a deposit to her bank account? Possibly, she can request a payment trace on the $472.40.

Anyway, it was an advance of the 2020 RRC. Based on 2020 she is not eligible for the RRC so you can't override the 2020 return for it.

No one falls under this: "The taxpayer made too much money in the 2020 tax year to receive this stimulus payment, but qualified with her 2019 tax return numbers."

You might be confusing the lookback for EITC, with the Recovery. 2019 is not a Qualification in lieu of 2020, for Recovery. It was used for Advances.

Perhaps it would help to review what is really happening for EIP “stimulus” funds: The funds were paid out as Advanced payment against a projection. The first two payouts were projected based on 2018 or 2019 tax returns, but the eligibility is part of tax year 2020 as Actuals. You use the 2020 return to reconcile what a person is entitled to, against what they got.

If the person is not a dependent in 2020, then they would be eligible for consideration as individual filers. That doesn't mean "not being claimed." It means "no longer qualifies as a dependent." You must correctly address whether they Can be Claimed as a dependent on someone else’s tax return.

The third payout which started in Jan 2021, has different eligibility rules as to dependents and this payout is a projection, using 2019 or 2020 tax returns, then reconciled against Actuals on the 2021 tax return.

You might want to bookmark these links and read the IRS guidance.

Interactive wizards portal includes one for determining dependency:

https://www.irs.gov/help/ita

And:

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-a-eip-eligibility

https://www.irs.gov/coronavirus/second-eip-faqs#Eligibility

https://www.irs.gov/newsroom/irs-is-issuing-third-round-of-economic-impact-payments

One for each of the three EIP “stimulus” payments.

Notice 1444 doesn't say "you are entitled," it says "you are receiving."  And it should state whether it was by direct deposit, debit card or check.