Non-coding RNAs have critical roles in biological processes, and RNA chaperones can promote their folding into the native shape required for their function. La proteins are a class of highly abundant RNA chaperones that contact pre-tRNAs and other RNA polymerase III transcripts via their common UUU-3′OH ends, as well as through less specific contacts associated with RNA chaperone activity. However, whether La proteins preferentially bind misfolded pre-tRNAs or instead engage all pre-tRNA substrates irrespective of their folding status is not known. La deletion in yeast is synthetically lethal when combined with the loss of tRNA modifications predicted to contribute to the native pre-tRNA fold, such as the N2, N2-dimethylation of G26 by the methyltransferase Trm1p. In this work, we identify G26 containing pre-tRNAs that misfold in the absence of Trm1p and/or La (Sla1p) in Schizosaccharomyces pombe cells, then test whether La preferentially associates with such tRNAs in vitro and in vivo. Our data suggest that La does not discriminate a native from misfolded RNA target, and highlights the potential challenges faced by RNA chaperones in preferentially binding defective substrates.