I think I've found some of the lost episodes

These include the performances too so I think these are the broadcasts that are being sought after? Some of the episode numbers are messed up but they are the correct lineup.

803 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+08/All+That+-+8x03+-+Yasmeen.MOV#

804 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+08/All+That+-+8x04+-+Jeffery+Licon.Jennifer+Love+Hewitt.MOV#

807 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+08/All+That+-+8x08+-+Nick+Carter.BBMak.MOV#

808 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+08/All+That+-+8x10+-+Britney+Spears.Justincase.MOV#

809 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/All+That+-+8x11+-+Nick+Cannon+%26+Orlando+Jones.Monica.mp4#

811 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+08/All+That+-+8x12+-+Matthew+Lillard.O-Town.MOV#

903 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x03+-+Da+RazKalz+Cru.mp4#

904 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x04+-+Third+Eye+Blind.MOV#

905 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x05+-+Fefe+Dobson.MOV#

906 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x06+-+Nikki+Cleary.MOV#

907 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x07+-+JC+Chasez.Drake+Bell.MOV#

908 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x08+-+OK+Go.MOV#

909 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x09+-+Britney+Spears.Nick+Cannon.MOV#

911 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+09/All+That+-+9x12+-+Nick+Lachey.MOV#

1001 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+10/All+That+-+10x03+-+Mario.mp4#

1002 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+10/All+That+-+10x04+-+Fantasia.mp4#

1003 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+10/All+That+-+10x05+-+Jesse+McCartney.mp4#

1004 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+10/All+That+-+10x06+-+JoJo.mp4#

1005 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+10/All+That+-+10x07+-+Tyler+Hilton.mp4#

1006 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+10/All+That+-+10x08+-+Drake+Bell.mp4#

1007 - https://archive.org/details/all-that-7x-01-frankie-muniz.-aaron-carter/Season+10/All+That+-+10x09+-+Morgan+Smith.mp4#