This seems to be the information that you are intersted in.
An LPR is never required to seek naturalization but if (s)he does desire it, the first thing to do is not loose LPR status.
FROM CBP website:
"I am a lawful permanent resident of the U.S., can I leave the U.S. multiple times and return?
If you are a lawful permanent resident (green card holder), you may leave the U.S. multiple times and reenter, as long as you do not intend to stay outside the U.S. for 1 year or more.
If you intend to stay outside the U.S. for 1 year or more, you must apply for a re-entry permit with U.S. Citizenship and Immigration Services (USCIS) prior to leaving the U.S. Re-entry permits are generally valid for 2 years from the date of issuance. Therefore, if you are outside of the U.S. longer than the date the permit was issued, you may be denied entry into the U.S.
To apply for a re-entry permit, you must file an Application for a Travel Document (I-131) with the USCIS. If you applied for permanent resident status, but are not yet officially a lawful permanent resident "green card holder" and you need to leave the U.S. on emergency, you must apply for and receive advance parole to leave the U.S. by filing a I-131 with USCIS. Information on how to file the I-131 is available on the USCIS Website.
If you are required to file documents prior to leaving the U.S., it is imperative that you do so, otherwise, you may be found inadmissible and denied reentry into the U.S. [This may lead to the completion of a form I-407, by the CBP Officer, in order to document abandonment/relinquishment of LPR status.]
If you are a green card holder and you do not stay outside the U.S. for 1 year or more, you should have either your green card (Form I-551), or your returning resident (SB-1) visa to re-enter the United States. You are not required to present your unexpired passport, however it is not a bad idea to carry it with you."
Presenting an expired greencard at a land or sea port of entry will cause delays and referral for secondary inspection and possibly deferred inspection after that.
Generally, an international air or sea carrier would refuse boarding if presented with an expired greencard unless you have a boarding letter or SB-1 visa also. A valid passport is required for non-contiguous travel or you would be denied boarding.
Certain cruises originating from and returning a U.S. port may be less strict.
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The basic requirements for the vast majority of naturalization applicants need only be satisfied within the final 5 years prior to filing an N-400, Application for Naturalization. The statutory period is only 3 years if all of that 3 years has been while married to and generally living with a USC spouse.
Certain factors prior to the "statutory period" may have an impact on naturalization eligibility, especially in determining good moral character (GMC). Look to some other thread for GMC info. A very late detection of initial entry fraud and possible initiation of Removal Proceedings can be a devasting result of filing for naturalization.
Physical presence within the U.S. is required to be equal to at least one half of the statutory period upon the filing date of the N-400. Continuous residence is a different requirement discussed below in the cited regulation.
Residence for general naturalization purposes:
8 CFR 316.5
(c) Disruption of continuity of residence —(1) Absence from the United States —(i) For continuous periods of between six (6) months and one (1) year. Absences from the United States for continuous periods of between six (6) months and one (1) year during the periods for which continuous residence is required under §316.2 (a)(3) and (a)(6) shall disrupt the continuity of such residence for purposes of this part unless the applicant can establish otherwise to the satisfaction of the Service. This finding remains valid even if the applicant did not apply for or otherwise request a nonresident classification for tax purposes, did not document an abandonment of lawful permanent resident status, and is still considered a lawful permanent resident under immigration laws. The types of documentation which may establish that the applicant did not disrupt the continuity of his or her residence in the United States during an extended absence include, but are not limited to, evidence that during the absence:
(A) The applicant did not terminate his or her employment in the United States;
(B) The applicant's immediate family remained in the United States;
(C) The applicant retained full access to his or her United States abode; or
(D) The applicant did not obtain employment while abroad.
(ii) For period in excess of one (1) year. Unless an applicant applies for benefits in accordance with §316.5(d), absences from the United States for a continuous period of one (1) year or more during the period for which continuous residence is required under §316.2 (a)(3) and (a)(5) shall disrupt the continuity of the applicant's residence. An applicant described in this paragraph who must satisfy a five-year statutory residence period may file an application for naturalization four years and one day following the date of the applicant's return to the United States to resume permanent residence. An applicant described in this paragraph who must satisfy a three-year statutory residence period may file an application for naturalization two years and one day following the date of the applicant's return to the United States to resume permanent residence.
(2) Claim of nonresident alien status for income tax purposes after lawful admission as a permanent resident. An applicant who is a lawfully admitted permanent resident of the United States, but who voluntarily claims nonresident alien status to qualify for special exemptions from income tax liability, or fails to file either federal or state income tax returns because he or she considers himself or herself to be a nonresident alien, raises a rebuttable presumption that the applicant has relinquished the privileges of permanent resident status in the United States.
(3) Removal and return. Any departure from the United States while under an order of removal (including previously issued orders of exclusion or deportation) terminates the applicant's status as a lawful permanent resident and, therefore, disrupts the continuity of residence for purposes of this part.
(4) Readmission after a deferred inspection or exclusion proceeding. An applicant who has been readmitted as a lawful permanent resident after a deferred inspection or by the immigration judge during exclusion proceedings shall satisfy the residence and physical presence requirements under §316.2 (a)(3), (a)(4), (a)(5), and (a)(6) in the same manner as any other applicant for naturalization.
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The remedy described in (ii) above is only found in the regulation, it is a gift from the immigration authorities as it does not exist in the statute in that form (it is derived from administrative discretionary authority in INA 316(b)). A straight reading of the statute would have an applicant start counting over from the beginning. As such, in that there is an early filing allowance of 3 months found at INA 334(a) this would result in only being able to file once achieving 4 years and 9 months (or 2 years and 9 months) residence. The regulatory remedy lets you apply after attaining 4 years and 1 day (or 2 years and 1 day) before filing after sustaining a disqualifying break in residence.