Concept:
A hydrogen-like species is a one-electron species.
So, to identify a hydrogen-like species, we check whether only one electron is present.
Step 1: Check \(\text{Li}^{2+}\).
Lithium has atomic number \(3\), so neutral Li has \(3\) electrons.
\[
\text{Li}^{2+} \Rightarrow 3-2=1 \text{ electron}
\]
So it is hydrogen-like.
Step 2: Check \(\text{Be}^{3+}\) and \(\text{He}^{+}\).
For \(\text{Be}^{3+}\):
\[
4-3=1 \text{ electron}
\]
For \(\text{He}^{+}\):
\[
2-1=1 \text{ electron}
\]
So both are hydrogen-like.
Step 3: Check \(\text{Li}^{+}\).
\[
\text{Li}^{+} \Rightarrow 3-1=2 \text{ electrons}
\]
So \(\text{Li}^{+}\) is not hydrogen-like.
Hence, the correct answer is:
\[
\boxed{(C)\ \text{Li}^{+}}
\]