To build the Lewis structure of $\mathrm{SeCl}_{3}^{+}$, we first need to determine the total number of valence electrons. Selenium (Se) has 6 valence electrons, and each chlorine (Cl) has 7 valence electrons. Since there are three chlorine atoms, we have:
\[
6 + 3 \times 7 = 27 \text{ valence electrons}
\]
However, because the molecule has a positive charge, we subtract one electron:
\[
27 - 1 = 26 \text{ valence electrons}
\]
Next, we draw the skeletal structure with selenium (Se) as the central atom and three chlorine (Cl) atoms bonded to it. Each bond represents 2 electrons.
After placing the bonds, we distribute the remaining electrons to satisfy the octet rule for each atom. Each Se-Cl bond uses 2 electrons, so:
\[
3 \times 2 = 6 \text{ electrons used in bonds}
\]
Subtracting these from the total valence electrons:
\[
26 - 6 = 20 \text{ electrons remaining}
\]
Each chlorine atom needs 8 electrons to complete its octet. Since each Cl already has 2 electrons from the bond, each needs 6 more electrons:
\[
3 \times 6 = 18 \text{ electrons for Cl atoms}
\]
Subtracting these from the remaining electrons:
\[
20 - 18 = 2 \text{ electrons remaining}
\]
The remaining 2 electrons are placed on the selenium atom.
Finally, we check the formal charges to ensure the structure is correct. The formal charge is calculated as:
\[
\text{Formal charge} = \text{Valence electrons} - \text{Non-bonding electrons} - \frac{\text{Bonding electrons}}{2}
\]
For selenium:
\[
6 - 2 - \frac{6}{2} = 6 - 2 - 3 = +1
\]
For each chlorine:
\[
7 - 6 - \frac{2}{2} = 7 - 6 - 1 = 0
\]
The positive charge is on the selenium atom, which matches the given $\mathrm{SeCl}_{3}^{+}$.
The Lewis structure of $\mathrm{SeCl}_{3}^{+}$ is:
\[
\begin{array}{c}
\text{Cl} \\
\vert \\
\text{Cl} - \text{Se}^{+} - \text{Cl} \\
\end{array}
\]
\(\boxed{\text{Lewis structure of } \mathrm{SeCl}_{3}^{+} \text{ is correct}}\)