  We have identified 189 candidate $z > 1.3$ protoclusters and clusters in the
LSST Deep Drilling Fields. This sample will enable the measurement of the metal
enrichment and star formation history of clusters during their early assembly
period through the direct measurement of the rate of supernovae identified
through the LSST. The protocluster sample was selected from galaxy
overdensities in a $Spitzer$/IRAC colour-selected sample using criteria that
were optimised for protocluster purity using a realistic lightcone. Our tests
reveal that $60-80\%$ of the identified candidates are likely to be genuine
protoclusters or clusters, which is corroborated by a $\sim4\sigma$ stacked
X-ray signal from these structures. We provide photometric redshift estimates
for 47 candidates which exhibit strong peaks in the photo-$z$ distribution of
their candidate members. However, the lack of a photo-$z$ peak does not mean a
candidate is not genuine, since we find a stacked X-ray signal of similar
significance from both the candidates that exhibit photo-$z$ peaks and those
that do not. Tests on the lightcone reveal that our pursuit of a pure sample of
protoclusters results in that sample being highly incomplete ($\sim4\%$) and
heavily biased towards larger, richer, more massive, and more centrally
concentrated protoclusters than the total protocluster population. Most
($\sim75\%$) of the selected protoclusters are likely to have a maximum
collapsed halo mass of between $10^{13}-10^{14}$ M$_{\odot}$, with only
$\sim25\%$ likely to be collapsed clusters above $10^{14}$ M$_{\odot}$.
However, the aforementioned bias ensures our sample is $\sim50\%$ complete for
structures that have already collapsed into clusters more massive than
$10^{14}$ M$_{\odot}$.
