"Even that she left lying"

It’s an instance of fronting, in which the writer moves a clause element from its usual position. Here, the object is moved from the normal position after the verb to a position in front of it. The effect is to emphasise ‘even that’, by placing it first, as well as ‘left lying’ by leaving it last. The unmarked version, ‘She left even that lying’, would instead emphasise ‘she’, which for literary reasons the writer clearly did not wish to do.

Fronting is generally a feature of formal prose, but the fronting of objects is not unusual in conversation in sentences such as ‘That I couldn’t tell you.’

When "that" is fronted as described, the intended meaning is not

She left everything lying in the fireplace, even the hair-tidy.

but

She did not remove anything, even the hair-tidy, from the fireplace.

The emphasis is upon the fact that even something so small and personal was not sufficient to overcome a general disposition to leave things behind.