Debugging STM32LF1xx low-power behavior
I would be tempted to use alternative debugging techniques such as status LEDs or a serial output displaying progress messages, with both the code concerned and the required peripherals' power enabled by build flags.  A lot of work has been done this way on systems where a breakpoint debugger was not available; used creatively it's extremely powerful and with the sub-minute build/flash/test cycles of today, pretty efficient.

Depending on how slow a clock rate you are dropping to, you might still be able to run a serial port at a standard baud rate (300 baud?, 75 baud with short abbreviations).  If not, you could do logging via a synchronous protocol like SPI where baud rate can usually be allowed to vary widely, and use another micro-controller as an SPI slave which in turn re-outputs asynchronous data to your PC at a standard baud rate.

It may also be useful to accessorize your SWD debugger with automated control of the reset line; the VL discovery boards do this for the on-board target processor, but it doesn't seem to be part of the SWD connector spec.  Also, if you have a firmware that goes into a low power mode quickly after boot, you can usually get the debugger going by holding down reset while commanding single-step mode, thus getting debug access before the mode switch can happen.