I visited this WHS in June 2019 and stayed a total of 5 nights here using it as my base for several short and long day trips to other WHS. To be fair, I wasn't expecting much from Lima and I chose to visit during 'garua' season as it happens to be the best season for the highlights of Peru further South.
That said, I couldn't not compare it to other WHS I had visited 'close' by such as Quito and Panama Viejo which were definitely better overall and more of an ensemble than the Peruvian capital. Lima's biggest problem is traffic, which doesn't even spare the main attraction of this WHS, Plaza de Armas. I enjoyed my numerous visits to the lively square at different times of the day and overall I enjoyed it the most in the evening when several 'cultural shows' took place to celebrate Afro-Peruvian communities. My personal highlight were the ornate wooden balconies of the Archbishop's Palace (photo) and the Torre Tagle Palace.
Moreover, Lima lacks a truly iconic building, monument or landmark and the majority of the places of interest are merely worth visiting but nothing very special, certainly not of outstanding universal value or unique. The Cathedral with Pizarro's tomb, St Martin's square, San Marcos Mansion's interior, the Rimac district, the Barrio Chino, the Santo Domingo Convent and Museum, the Government Palace, etc. are worth seeing but none would be must-sees to justify a revisit (if not a visit in the first place!). The marble UNESCO inscription plaque can be seen under the yellow colonnade in the main square.
The Church and Convent of San Francisco and its 'catacombs' (no photography allowed) would classify as a must-see in my books but again no OUV and not unique, as much better ones exist all over Europe. This site was the main reason Lima got inscribed back in 1988 and although the rest of the 'historic centre' was later added in 1991 through an extension, in my opinion it is Peru's least interesting WHS for now. An old bar/restaurant (Cordano) just next to the Church of San Francisco is worth mentioning as it is like an institution for many locals who work in the heart of Lima's city centre and it's great for a pint of beer or a Pisco Sour!