All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
First of all, we ask Allaah to facilitate your matters and to give you a way out of all your difficulties. If you supplicate Allaah with the supplication that was reported from the Prophet in this regard, then this is good. Please refer to fatwa 142905.
As regards what you asked about, which is buying a lottery ticket, then the answer is that it is not permissible for you to buy a lottery ticket or gamble in order to repay your debt. It is enough that you be determined to repay it whenever you become able to do so and Allaah will help you repay it.
If you die before repaying your debt, then we hope that Allaah will repay it on your behalf and please your creditors. The evidence about this is the hadeeth in which the Prophet said, “Whoever takes people's money while intending to repay it, Allaah will help him repay it, and whoever takes people's money while intending to spoil it (not repay), then Allaah will spoil him (i.e. spoil his wealth and punish him in the hereafter).” [Al-Bukhari]
Ibn Hajar said, “…If a person dies before fulfilling his debt without any negligence on his part, such as if he is in financial difficulties, for example, or that he suddenly dies while he has hidden money and had the intention to repay his debt but was unable to do so in this worldly life, then it appears, in this case, that he is free from any liability in the Hereafter and that his good deeds will not be taken from him and given to the creditor; rather, Allaah will repay the creditor on his behalf.”
For more benefit on the necessity that makes it permissible to commit what is forbidden, please refer to fatwa 263158.
Allaah knows best.