Do any methods exist (or are in the process of development) for investigating transcript data without lysing the cells, i.e, destroying the sample?
Answer: There are no methods that exist for investigating transcript data inside a cell without destroying the cell. Separating RNA from cells requires essentially destroying the cells and using a chemical cocktail to split its constituent components.
Alternative 1: One option is to investigate extracellular transcripts of living cells is to centrifuge cells in culture and isolating RNA from the growth media supernatant . Cell-free DNA and cell-free RNA are hot topics in contemporary biology and bioinformatics as a potential source for disease biomarkers. 
Alternative 2: Another option to monitor a transcript from a living cell is to use a transgenic construct with a reporter molecule like luciferase or a fluorescent protein to produce light or become fluorescent when a promotor is activated [3, 4]. This does not directly measure transcript quantity but answers a similar question: how does transcription change in a living cell?
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 Yu, X. M., Wu, Y. C., Liu, X., Huang, X. C., Hou, X. X., Wang, J. L., ... & Ling, Z. Q. (2016). Cell-Free RNA content in peripheral blood as potential biomarkers for detecting circulating tumor cells in non-small cell lung carcinoma. International journal of molecular sciences, 17(11), 1845.
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