Link integrity test pulse vs carrier signal
Beginning from 10BASE-T, there is no CDMA/CD in Ethernet because (and while) the underlaying PMA/PMD provides the PCS (providing the service interface for the MAC) with a full duplex data transmission mechanism. In 10BASE-T, 100BASE-TX, 1000BASE-X, 1000BASE-T, etc., the half duplex mode of operation, i.e. providing CRS and CD signals by the PHY to its MAC, is speculatively simulated in the PHY by itself like the following:


carrier sense := rx activity or tx activity
collision detect := rx activity and tx activity


(Be careful here and remember that rx activity as well as tx activity are on the medium side while carrier sense is on the PHY service interface, i.e. MAC, side.)

Returning to your counters, they (could) show how the actions over the PHY (being taken by the MAC serviced) correlate/correspond with the actions under the PHY (happening at the medium) and may (could) be like the following: 


lost carrier counter increments when carrier sense transits from HIGH to LOW while TX_EN is HIGH (generally speaking, it's implementation dependent and could be sole TX_EN, sole RX_DV, or combination thereof)
no carrier counter increments when TX_EN transits from LOW to HIGH while carrier sense is LOW (it's also implementation dependent and could be other any)


In other words, the first counter indicates how many times the link fails while a packet was transmitted and/or received---collectively, presented---at the medium, and the second counter indicates how many times the MAC attempts to send a packet while there was no  physical link. 

An yes, in 10BASE-T (and in EEE today) FLPs are generated while the medium is idle, but this is not the case as it is shown above.