Can I stay lawfully in US if I marry to a lawful permanent resident?

A marriage in itself does not provide any Immigration benefits.

Generally, a Permanent Resident who marries a foreign national in the U.S. who is present with a valid nonimmigrant visa may sponsor the spouse in an application to adjust status, in the Family-Sponsored Second Preference (F2A) visa category to become a Permanent Resident. There is a backlog for visas in this category, however, and the beneficiary spouse would not be authorized to remain in the U.S. while awaiting availability of a visa unless he/she had another valid nonimmigrant visa. The same analysis does not apply to a foreign national who becomes married to a U.S. citizen. In that event, there is no backlog for visas and such a case may proceed even if the beneficiary spouse may have overstayed his/her initial nonimmigrant visa. It would be wise for you and your Permanent Resident spouse to consult an immigration attorney who, after learning all of the relevant information about each of you, could advise about immigration eligibilities, options and strategies, and who then could offer legal representation in the often complex application process.