What date did she leave the UK?
Her ILR will be valid for 2 years after moving away from the UK, so if it has been less than 2 years since she moved back to the US, then she can just return to live in the UK using her ILR (as long as she returns before the 2 years are up).
However, if it has been more than 2 years since she left the UK, her ILR will now be invalid, which means that in order to move back to the UK again, she will need to start the immigration process from scratch and qualify for a visa to return (i.e. student visa, work visa, fiance/spousal visa if you were to get married).
In order for her to qualify for UK citizenship, she must:
1) be a current UK resident
AND
2) hold a valid ILR
AND
3) have not been outside the UK for more than 450 days in the last 5 years, with no more than 90 of those days being in the last 12 months before applying
AND
4) have been physically in the UK exactly 5 years prior to the date she applies for UK citizenship