If the person living with you is a close relative* for whom you do not receive Child Benefit, then they will be classed as a non-dependant even if you regard them as a lodger.
To be classed as a lodger the person living with you must not be a close relative*, and must be paying you for accommodation and/or meals (‘board’) on a commercial basis. The local council (or DWP if you are on Universal Credit) will want to see some proof of the commercial basis of the arrangement to be convinced they are a lodger- such as a rent book and/or tenancy agreement. It is unlikely they will accept a person as a lodger if they were previously classed as a non-dependant.
Under Housing Benefit rules, any money over £20 per week which the lodger pays you for their accommodation can affect your benefit entitlements. If you are getting Universal Credit, none of the money you receive from them is taken into account – but they are not allocated a bedroom under the Universal Credit Bedroom Tax rules.
*Close relative means parent, parent-in-law, son, son-in-law, daughter, daughter-in-law, step-parent, step-son, step-daughter, brother, sister or the spouse or partner of any of these people.