וַתֹּ֙אמֶר֙ בִּ֣י אֲדֹנִ֔י חֵ֥י נַפְשְׁךָ֖ אֲדֹנִ֑י אֲנִ֣י הָאִשָּׁ֗ה הַנִּצֶּ֤בֶת עִמְּכָה֙ בָּזֶ֔ה לְהִתְפַּלֵּ֖ל אֶל־יְהוָֽה׃
И она сказала: 'О мой господин, так как твоя душа живет, мой господин, я та женщина, которая стояла рядом с тобой здесь, молясь Господу.
Rashi
Please my lord. Take care of him, that he become your disciple. But according to the Midrash of our Sages, [she asked of Eili] not to punish him with death.
Radak
Please, my lord: It is a matter of a supplication and a request - like its translation [in Targum Yonatan], "please, my master" - as you live, that you should keep your eyes upon this lad and teach him, for "I am the woman" who prayed to the Lord.
Metzudat David
Please, my lord: She requested from Eli, and made him swear by his own soul, to keep his eye on the lad.