salaam brothers and sisters, my best friend told me she was lesbian, and she's a muslim. What's the punishment for her? if she has any sexual relationships, then?
It depends. A person who claims to be a lesbian may fall under either of the following cases:
She believes that performing homosexual acts is justified and appropriate. This falls under kufr as it is denial of an established part of Islam.
Punishment in the afterlife: The punishment for unrepentant kufr is eternal hell fire. However if she changes her views and seeks forgiveness during her lifetime, then she may be forgiven. (Quran 2:217)
Punishment in this life: The legal punishment is execution (for apostasy), provided that the requirements of evidence are met. A minority does not execute female apostates rather imprisons them and forces them to repent or remain imprisoned till death. (Bukhari)
She believes homosexuality to be wrong, however she commits homosexual acts because of failing to control her desires. This is a major sin, but is not kufr, according to the ahl al-Sunnah. It is similar to other sins like a muslim performing adultery, theft etc. while accepting that these acts are inappropriate.
Punishment in the afterlife: She can be forgiven if she repents. If she does not repent then the punishment in the afterlife is left to Allah's will, He may forgive her or punish her for a finite time in Hell fire. She is also eligible for receiving the benefit of intercession. Eventually she would be forgiven and admitted into paradise as long as she was a Muslim at the time of death. (Quran 4:48, Bukhari)
Punishment in this world: The legal punishment is a ta'zir if evidence exists that she has done the act. In a ta'zir it is left to the discretion of the judge to enforce any punishment which he feels is appropriate and adequate. A ta'zir is the default punishment for any sin which does not have an explicitly prescribed punishment. Ta'zir punishments may include for example imprisonment or whipping etc.
She feels sexual attraction towards other females, but does not act on these desires. This does not get any punishment as she has not done anything wrong. Similar to how a person is not punished for merely having the temptation to perform adultery, murder, theft etc.
واتفقوا ... فان من جحد شيئا مما ذكرنا أو شك في شيء منه ومات على ذلك فانه كافر مشرك مخلد في النار أبدا
[i.e. There is consensus that anyone who rejects any part of Islam is a Kafir and Mushrik who remains in hell forever]
واتفقوا أن سحق المرأة للمرأة حرام ... أنه لا حد في شيء من ذلك كله
[i.e. There is consensus that the sexual act done by lesbians is Haram, but that does not get the Hadd]
أجمع العلماء على أن التعزير مشروع في كل معصية لا حد فيها ولا كفارة والمعاصي فرعان: ترك واجب وفعل محرم
[i.e. There is consensus that every sinful act which does not have a hadd punishment gets a ta'zir punishment]
اتفق أهل السنة على أن المؤمن لا يخرج عن الإيمان بارتكاب شيء من الكبائر إذا لم يعتقد إباحتها، وإذا عمل شيئا منها، فمات قبل التوبة، لا يخلد في النار، كما جاء به الحديث، بل هو إلى الله، إن شاء عفا عنه، وإن شاء عاقبه بقدر ذنوبه، ثم أدخله الجنة برحمته
[i.e. The Ahl al-Sunnah are in consensus that a person who performs a sin remains a Muslim unless he\she believes the act to be lawful, And hence such a person remains eligible for forgiveness from Allah]
واتفقوا أن التوبة من الكفر مقبولة ما لم يوقن الإنسان بالموت بالمعاينة ومن الزنا ومن فعل قوم لوط ومن شرب الخمر ومن كل معصية بين المرء وربه تعالى
[i.e. There is consensus that repentance may be accepted for all sins if it is done before death, including from sins like kufr and homosexual acts]