The assessment of patient safety is to be undertaken at Wishaw General and Monklands General Hospitals, which both had higher than average mortality rates during the last four months.
Hairmyres Hospital in East Kilbride will also be probed as part of the Healthcare Improvement Scotland (HIS) investigation.
Latest figures published today show that while overall hospital mortality has fallen over the last five years, Wishaw and Monklands have high ratios for the latest quarter.
NHS Scotland Clinical Director, Professor Jason Leitch, has asked HIS to work with NHS Lanarkshire to examine their approach to patient safety.
Prof Leitch said: "We expect all health boards to ensure patient safety is their top priority and the Scottish Patient Safety Programme has been working for over five years to deliver ways to make healthcare safer.
"Although a high hospital standardised mortality rate (HSMR) is not by itself a definitive measure of the quality and safety of care, it serves as an important prompt for further investigation.
"Where HSMR suggests a potential issue, a health board must be able to demonstrate that it is taking appropriate action to investigate and resolve any problems found to be causing a higher than expected HSMR, and it is reassuring that NHS Lanarkshire is already working on an action plan to address this.
"That is why I have also commissioned HIS to undertake a rapid assessment, in partnership with NHS Lanarkshire, of the reasons behind the HSMR figures in Lanarkshire and to see if the improvement measures in place can be strengthened and accelerated."
The review will help to understand if there are any underlying issues which require additional support to be resolved.
Dr Iain Wallace, Medical Director for NHS Lanarkshire, said: "We very much welcome the support and involvement of HIS to undertake an assessment of the local action plans we are progressing, along with their detailed review to identify any further improvement measures that can be implemented."