Apparently it means that he will lose
his daughter to someone, meaning the daughter will marry or go away with that other person and will no longer be close to the father. It seems Shakespeare used to write "loose" instead of "lose" (Oxford Dict. Unabridged):
4.4 absol. or intr. a.4.a To suffer loss; to cease to possess something; to be deprived of or part with some of his or its possessions, attributes, or qualities; to become deteriorated or incur disadvantage.
c 1230 Hali Meid. 41 Ha beon eauer feard for to losen [elsewhere, and here in MS. Bodl. leosen]. c 1470 Henry Wallace iv. 336 Now want, now has; now loss, now can wyn. 1596 Shakes. Tam. Shr. Induct. ii. 101 Thou shalt not loose by it.
1611 Bible Eccl. iii. 6 A time to get, and a time to lose. 1643 J. Burroughes Exp. Hosea iv. (1652) 75 There is nothing lost in being willing to lose for God. 1697 Dryden Ded. Æneis Ess. (ed. Ker) II. 229 Thus, by gaining abroad, he lost at home. 1838 Macaulay Temple Ess. (1887) 440 He never put himself prominently before the public eye, except at conjunctures when he was almost certain to gain and could not possibly lose. 1850 Tennyson In Mem. xxvii, 'Tis better to have loved and lost Than never to have loved at all. 1895 George Battles Eng. Hist. 313 Fortunately the Sikhs had lost so severely that no evil consequences followed. 1898 Folk-Lore Sept. 198 The other was undertaken by a publisher, who lost on it. Mod. Both armies lost heavily.