Electronic configuration for these ions is:
$Li ^{+}: 1 s ^2$
$Be ^{+}: 1 s ^2\, 2 s ^1$
$B ^{+}: 1 s ^2\, 2 s ^2$
For, lithium and boron, electron is to be ejected from fully filled stable shells.
Further, it is difficult to remove electron from is shell of $Li$ because it is closer to the nucleus as compared to $2 s$ shell of $B$. It is much easier to remove electron from $Be$ because it will attain stable electronic configuration after losing this electron.
Thus, order is $Li \,> \,B\, >\, Be$
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