From the way this question is phrased, it appears that the lac repair was done by an ER provider and, therefore, the clinic is not part of the global care. If the clinic provider did the lac repair, irregardless of where the repair was done (in-patient, ER, clinic), then the clinic provider is paid for the global package of the lac repair. In this case, whether or not you can bill for a complication depends on two things - 1 - the extent of work provided for the complication and 2 - the payer.
CPT defines the global package to include "typical postoperative follow-up care". Since it is not "typical" for a patient to have a complication, from CPT's definition care for a complication would not be included in the global package. However, you need to use a modifier to let the payer that know that the care for this complication is not "typical" postoperative follow-up and that modifier is -24. Modifier -24 is described as "Significant, separately identifiable . . . ". Be careful about that "significant" part. If the documentation does support an E&M code for the history, exam and/or MDM (2 of 3) specific to the complication (and not the routine post op care), then this modifier should not be used.
However, CMS does not accept the CPT definition for billing an E&M during the global period. They claim that they recognize that a certain percentage of each procedure will have minor complications and have factored this into the RVUs assigned to each CPT code. Therefore, to use modifier -24, CMS says that the E&M service must have nothing to do with the surgery or the reason for the surgery.
So, if the payer is Medicare in your case, you cannot bill for the E&M associated with this complication.
Hope this helps,
Karen Hill, CPC, CPB, CPMA, CPC-I
AHIMA Approved ICD-10-CM Trainer
P.S. There is a great on-demand webinar offered by AAPC about modifiers and the global package.