Lawwām comes from the root l-w-m, ‘to blame.’ While lāʾim means a reproacher, the faʿʿāl pattern may intensify the action or imply repeated reproach.
The poet evokes not a single complaint but a setting of persistent scrutiny. The phrase bi-ḥājatin identifies the need for which he might be criticised, while the suffix -hā refers back to that need.