  The $\Lambda^0_b \to D^+ D^- \Lambda$ decay is observed for the first time
using proton-proton collision data collected by the LHCb experiment at a
center-of-mass energy of $13 \mathrm{TeV}$, corresponding to an integrated
luminosity of $5.3 \mathrm{fb}^{-1}$. Using the $B^0 \to D^+ D^-
K_{\mathrm{S}}^0$ decay as a reference channel, the product of the relative
production cross-section and decay branching fractions is measured to be $$
{\cal R}=\frac{\sigma_{\Lambda^0_b}}{\sigma_{B^0}} \times \frac{{\cal
B}(\Lambda^0_b \to D^+ D^- \Lambda)}{{\cal B}(B^0 \to D^+ D^-
K_{\mathrm{S}}^0)}=0.179 \pm 0.022 \pm 0.014 $$ where the first uncertainty is
statistical and the second is systematic. The known branching fraction of the
reference channel, ${\cal B}(B^0 \to D^+ D^- K_{\mathrm{S}}^0)$, and the
cross-section ratio, $\sigma_{\Lambda^0_b} / \sigma_{B^0}$, previously measured
by $\mathrm{LHCb}$ are used to derive the branching fraction of the
$\Lambda^0_b \to D^+ D^- \Lambda$ decay $$ {\cal B}(\Lambda^0_b \to D^+ D^-
\Lambda)=(1.24 \pm 0.15 \pm 0.10 \pm 0.28 \pm 0.11) \times 10^{-4}, $$ where
the third and fourth contributions are due to uncertainties of ${\cal B}(B^0
\to D^+ D^- K_{\mathrm{S}}^0)$ and $\sigma_{\Lambda^0_b} / \sigma_{B^0}$,
respectively. Inspection of the $D^+ \Lambda$ and $D^+ D^-$ invariant-mass
distributions suggests a rich presence of intermediate resonances in the decay.
The $\Lambda^0_b \to D^{*+} D^- \Lambda$ decay is also observed for the first
time as a partially reconstructed component in the $D^+ D^- \Lambda$ invariant
mass spectrum.
