During eukaryotic DNA replication, DNA polymerase alpha/primase (Pol α) initiates synthesis on both the leading and lagging strands. It is unknown whether leading- and lagging-strand priming are mechanistically identical, and whether Pol α associates processively or distributively with the replisome. Here, we titrate cellular levels of Pol α in S. cerevisiae and analyze Okazaki fragments to study both replication initiation and ongoing lagging-strand synthesis in vivo. We observe that both Okazaki fragment initiation and the productive firing of replication origins are sensitive to Pol α abundance, and that both processes are disrupted at similar Pol α concentrations. When the replisome adaptor protein Ctf4 is absent or cannot interact with Pol α, lagging-strand initiation is impaired at Pol α concentrations that still support normal origin firing. Additionally, we observe that activation of the checkpoint becomes essential for viability upon severe depletion of Pol α. Using strains in which the Pol α-Ctf4 interaction is disrupted, we demonstrate that this checkpoint requirement is not solely caused by reduced lagging-strand priming. Our results suggest that Pol α recruitment for replication initiation and ongoing lagging-strand priming are distinctly sensitive to the presence of Ctf4. We propose that the global changes we observe in Okazaki fragment length and origin firing efficiency are consistent with distributive association of Pol α at the replication fork, at least when Pol α is limiting.