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 $Li \,> \,B\, >\, Be$