The transcript ID is defined by the authors of MiTranscriptome. In OncoLnc everything labeled a lncRNA is from the MiTranscriptome beta dataset. You can browse the transcripts at their data portal: http://mitranscriptome.org/, and also search their browser. If you use their search box you can only type in the gene name, not the transcript ID. For example, the first lncRNA in their browser has the name A2M-AS1.1, and the transcript ID T073329, and you would have had to type in A2M-AS1.1 to find it.
MiTranscriptome beta used the same raw data that the TCGA used for their read counts, but the TCGA consortium only mapped reads to transcripts which were known at the time. As a result, there is some overlap between the lncRNAs in MiTranscriptome beta and the Tier 3 TCGA genes (which I refer to as mRNAs in OncoLnc), and these will have the same gene names, but MiTranscriptome will have a transcript ID while TCGA genes will have an Entrez ID.
If there is a specific lncRNA you are looking for I would recommend browsing MiTrancriptome beta for it and then typing in the transcript ID into OncoLnc. If MiTranscriptome beta and therefore OncoLnc does not have the lncRNA you are looking for you could also try exploring TANRIC: http://ibl.mdanderson.org/tanric/_design/basic/index.html, which also has survival analyses.