Staying outside the US for an extended time does not cause the LPR status to be abandoned. Nor does failing to renew a 10 yr GC. Not does failing to file taxes. LPR status must either be abandoned by v the use of v the I407 by the GC holder or by a decision of an immigration judge.
If the airline accepts the expired GC and the OP gets to fly, expect significant questioning at POE. Refuse to sign the 407 when offered by CBP, request to be able to come before a judge, get a good immigration lawyer and work very hard at establishing the evidence of actually living in the US. This is not a minor nor simple situation.