Don't use the "StateImages" and the "StateIndex", they are for particular images depending on the "state" (checked or whatever) of the item. The normal icons are taken from the "SmallImages"/"LargeImages", and are selected according to the "ImageIndex".
I'm pasting here the lfm file which works fine for me:
object Form1: TForm1
Left = 369
Height = 240
Top = 134
Width = 320
Caption = 'Form1'
ClientHeight = 240
ClientWidth = 320
LCLVersion = '1.5'
object ListView1: TListView
Left = 0
Height = 240
Top = 0
Width = 320
Align = alClient
Columns = <>
Items.LazData = {
9E0000000600000000000000FFFFFFFFFFFFFFFF00000000050000004974656D
3000000000FFFFFFFFFFFFFFFF00000000050000004974656D3100000000FFFF
FFFFFFFFFFFF00000000050000004974656D3200000000FFFFFFFFFFFFFFFF00
000000050000004974656D3300000000FFFFFFFFFFFFFFFF0000000005000000
4974656D3400000000FFFFFFFFFFFFFFFF00000000050000004974656D35
}
LargeImages = ImageList1
SmallImages = ImageList1
TabOrder = 0
ViewStyle = vsIcon
end
object ImageList1: TImageList
left = 88
top = 152
Bitmap = {
4C690100000010000000100000007A7A7ACBC2C2C2FEC2C2C2FDC2C2C2FDC2C2
C2FDC2C2C2FDC2C2C2FDC2C2C2FDC2C2C2FDC2C2C2FDC2C2C2FDC3C3C3FDC4C4
C4FDCACACAFE8A8A8AF50E0E0E65B8B8B8F8FFFFFFFFFEFEFEFFFBFBFBFFFBFB
FBFFFBFBFBFFFBFBFBFFF8F8F8FFFAFAFAFFFBFBFBFFF3F3F3FFF0F0F0FFEDED
EDFFFEFEFEFFD3D3D3FF1F1F1FC2B7B7B7F6FFFFFFFFF1F1F1FFEBEBEBFFECEC
ECFFEDEDEDFFE8E8E8FFE4E4E4FFEAEAEAFFF1F1F1FFECECECFFEBEBEBFFE8E8
E8FFF7F7F7FFCFCFCFFF1E1E1EC2B3B3B3F6FFFFFFFFE5E5E5FFD6D6D6FFE1E1
E1FFE2E2E2FFD1D1D1FFD2D2D2FFE2E2E2FFECECECFFF1F1F1FFEDEDEDFFECEC
ECFFF9F9F9FFCDCDCDFF1D1D1DC1B2B2B2F6FFFFFFFFE9E9E9FFD4D4D4FFCBCB
CBFFCCCCCCFFC9C9C9FFC7C7C7FFCFCFCFFFE9E9E9FFF1F1F1FFEDEDEDFFEAEA
EAFFF6F6F6FFCBCBCBFF1C1C1CC1B2B2B2F6FFFFFFFFF3F3F3FFF1F1F1FFEFEF
EFFFEFEFEFFFEDEDEDFFECECECFFEBEBEBFFE9E9E9FFE7E7E7FFE5E5E5FFE6E6
E6FFF6F6F6FFC9C9C9FF1B1B1BC1B0B0B0F6FBFBFBFFE3E3E3FFE0E0E0FFE0E0
E0FFE2E2E2FFDFDFDFFFDBDBDBFFDEDEDEFFDEDEDEFFD9D9D9FFD5D5D5FFDADA
DAFFF5F5F5FFC9C9C9FF1B1B1BC1AFAFAFF6FAFAFAFFE5E5E5FFE3E3E3FFE0E0
E0FFE0E0E0FFDFDFDFFFDDDDDDFFDCDCDCFFDEDEDEFFD8D8D8FFDADADAFFE1E1
E1FFF4F4F4FFC7C7C7FF1B1B1BC1ADADADF6FAFAFAFFE3E3E3FFDFDFDFFFE0E0
E0FFE1E1E1FFDCDCDCFFD9D9D9FFDBDBDBFFDBDBDBFFD8D8D8FFD5D5D5FFDDDD
DDFFF3F3F3FFC5C5C5FF1A1A1AC1ACACACF6F8F8F8FFE1E1E1FFE1E1E1FFDCDC
DCFFDCDCDCFFE2E2E2FFDFDFDFFFE2E2E2FFE2E2E2FFDDDDDDFFD9D9D9FFDADA
DAFFF0F0F0FFC3C3C3FF1A1A1AC1AAAAAAF6FBFBFBFFE6E6E6FFE3E3E3FFE2E2
E2FFE3E3E3FFE5E5E5FFE6E6E6FFE4E4E4FFE2E2E2FFE1E1E1FFDFDFDFFFE0E0
E0FFF0F0F0FFC1C1C1FF191919C1A9A9A9F6F8F8F8FFDEDEDEFFE1E1E1FFE3E3
E3FFE2E2E2FFDFDFDFFFDDDDDDFFDDDDDDFFDBDBDBFFDADADAFFDADADAFFDDDD
DDFFEFEFEFFFC0C0C0FF191919C1A8A8A8F6F8F8F8FFDCDCDCFFDEDEDEFFDEDE
DEFFDCDCDCFFDDDDDDFFD9D9D9FFDBDBDBFFDFDFDFFFE0E0E0FFE2E2E2FFDEDE
DEFFECECECFFBDBDBDFF181818C1AAAAAAF7FFFFFFFFF3F3F3FFF2F2F2FFF0F0
F0FFEFEFEFFFEEEEEEFFEDEDEDFFEAEAEAFFE1E1E1FFDCDCDCFFDCDCDCFFDEDE
DEFFF3F3F3FFC6C6C6FF191919C3787878EEE2E2E2FFDDDDDDFFDBDBDBFFDADA
DAFFD9D9D9FFD9D9D9FFD8D8D8FFD6D6D6FFD1D1D1FFCFCFCFFFD0D0D0FFD0D0
D0FFDEDEDEFF999999FF0C0C0CBD0B0B0B00252525C7252525CC242424CA2424
24CA242424CA242424CA252525CA252525CA262626CA262626CA252525CA2525
25CA262626CE111111C300000055
}
end
end