Honestly lying that you're an LPR can only bite you in the ass if you say it to a CBP agent while trying to seek entry back into the US. Other than that, there's no penalties in the law for lying about it.
Do not ever lie that you're a USC in ANY context though. That shit will make you inadmissible for life with only something like a U-visa being able to save you.
__________________
I-360 (VAWA) filed: 08/21/2018 RFE: 02/27/2020 Due: 05/25/2020 Submitted: 05/21/2020
I-360 approved: 11/10/2020
Motion to recalendar filed: 07/29/2022 Motion to recalendar approved: 08/30/2022 Dismissed: 06/07/2023
I-485 filed: 06/17/2023 I-485 Interview: 4/29/2024 I-485 approved: TBD