Levi should run away before the psak din is issued
He can not kill the eidim as its the Beis din of 23 who issue the final psak and are responsible for his death and they are not killing him deceitfully. The eidim are not responsible because "ein shliach lidvar aveira" as quoted in Gemoro kidushin 43a "ho'omeir lishlucho tzei vaharog es hanefesh hu chayav vesholchov potur" - one who sends an emissary to kill someone, the emisary is liable and the sender is exempt. the beis din issue the killing and not the eidim even though the beis din are acting through the eidus of the eidim so you cant kill the eidim for the beis din's killing.
The eidim can only be killed if they are found zommeimim (in another place at the time of testimony) by 2 other eidim who saw them in another place at the time of their testimony. See Makos 2a
After the Psak Din of sentencing to death There is an unfortunate case about the son of Shimon ben Shetach being framed for a capital punishment in the Gemoro yerushalmi sanhedrin 6:3,
אמר לו שמעון בן שטח אראה בנחמם אם לא מעלים עליך כאילו שפכת דם נקי באותה שעה קיבל עליו שלא יורה אלא מפי שמעון בן שטח שמעון בן שטח היו ידיו חמומות אתא סיעת ליצנין אמרי הבו עיציה ניסהוד על ברי וניקטליני אסהידו עלוי ונגמר דינו ליהרג כי נפק למיתקטל אמרי ליה מרי שיקרין אנן בעא אבוי מחזרתיה א"ל אבא אם ביקשתה לבוא תשועה על ידך עשה אותי כאסקופה - there was false witnesses brought against Shimon's son, whom they accused of a crime which involved capital punishment; and as a result of this charge he was sentenced to death. While on the way to the place of execution, the witnesses recanted their testimony. Shimon ben Shetach sought to have the case reopened. Shimon's son protested that, according to the Law, kivain shehigid shuv aino chozer umagid(a witness must not be believed when he withdraws a former statement), and he said to his father, "If you see to bring about salvation, then consider me as an initiation [towards that goal].
This case where The Son of Shimon ben Shetach did not flee, was after the Gemar din,at which point He was Mechuyav to be moser nefesh to do the Mitzva of Devarim 17,11 ועל המשפט אשר יאמרו לך תעשה - "The Judgment which They (the Beis din) tell you shall you do" in front of a minian of people ( 23 sanhedirin and 2 eidim) as it says וְנִקְדַּשְׁתִּי בְּתוֹךְ בְּנֵי יִשְׂרָאֵל and in Sanhedrin 74a it explains one of the meanings of this posuk:א"ר יוחנן אפי' שלא בשעת גזרת מלכות לא אמרו אלא בצינעא האבל בפרהסיא אפי' מצוה קלה יהרג ואל יעבור In public even a small Mitzva must not be transgressed and it says אמר רבי יוחנן אין פרהסיא פחותה מעשרה בני אדם פשיטא ישראלים בעינן דכתיב (ויקרא כב, לב) ונקדשתי בתוך בני ישראל in public means 10 jews. Her ther are at least 23 as it says sanhedrin 2a with dinei nefashos.
However before the pesak din if he runs away he saves his life and is not going against the pesak of Beis din because it hasn't come out yet.
A proof of this is that Shaul considerred Dovid chayav misa for being Moreid Bemalchus when he was anointed by Shmuel and was on the run for many years but had never been indicted formally in Beis din as he was always one step ahead (as indicated in the haftora "Machar chodesh") .