Isoelectronic species are atoms or ions that contain the same number of electrons.

1. Analyze Beryllium ion ($Be^{2+}$): Beryllium has atomic number $Z=4$. The $+2$ charge indicates the loss of 2 electrons. Therefore, the number of electrons in $Be^{2+}$ is $4 - 2 = 2$ electrons.
2. Analyze the options: $H^+$ (Protium ion, $Z=1$): $1 - 1 = 0$ electrons. $Li^+$ (Lithium ion, $Z=3$): $3 - 1 = 2$ electrons. $Na^+$ (Sodium ion, $Z=11$): $11 - 1 = 10$ electrons. $Mg^{2+}$ (Magnesium ion, $Z=12$): $12 - 2 = 10$ electrons.

Since $Li^+$ contains 2 electrons, it is isoelectronic with $Be^{2+}$ (both having the stable duplet configuration of Helium, $1s^2$).