The Lift and Escalator industry is somewhat behind in its implementation of PUWER.
The Lift and Escalator Association (LEA) guidance has recently been updated and endorsed by HSE.
As the lift is your responsibility, you must ensure that it is safe.
You must also ensure safe access and egress to the lift pit; this should be a fixed ladder to ISO 14122; if that cannot be provided due to the constraints of the installation of the lift, then a removable ladder is your only option, again to ISO 1412. It is your responsibility, not the maintenance provider, as it is part of your building.
If there is a danger of a fall from height at the top of the lift car, then it is your responsibility to prevent this; the lift belongs to you, not your maintenance provider. The balustrade needs to be again per the relevant harmonised or designated standards if that is the most suitable. This time it could be ISO 14122 or ISO 14120, depending on the design. If this guard can pose a hazard to persons or equipment when not in a suitable position, it needs to have an interlock; this needs to be designed and implemented again following the relevant standards.
You need to ensure that it is safe for your maintainer's personnel to enter the lift pit below the lift. You must ensure that the lift can not under any circumstances fall and injure the personnel. Preventing the lift from falling may well require a prop or other means of preventing the uncontrolled descent of the lift when under maintenance. Note that some safety features in place during regular operation may be disabled when the lift is being maintained, for them to be maintained or repaired themselves.
The lift is in your building and is your responsibility; thus, it is your responsibility to provide this safety equipment, not the maintainer.
Your first port of call would be the Lifts Directive, 2014/33/EU as transposed into UK legislation as SI/2016/1093. Annexe I of this legislation also refers to Annexe I in the Machinery Directive / Supply of Machinery (Safety) Regulations for any hazards not explicitly covered in the Lifts Directive. Along obviously with PUWER as it is an existing lift installation. PUWER guides you to using the Harmonised (to be Designated) standards for compliance in designing new safety features such as guards and ladders. Other relevant standards that would need to be considered during the design and implementation of any updates would be the EN 81 series, ISO 13849-1 & -2, ISO 14118, EN 60204-1 possibly. EN 62061 potentially, the others are listed in the Offical Journal of the EU, and these can then be traced to the BSI website, where they will be indicated as Designated.
There is also free to download guidance on the Europa website listing the Harmonised standards to the Lifts and Machinery Directives, along with a guide to the Lifts directive. The LEA guidance for lift owners will also support my comments. This is free to download from their website.