The 12-month brief includes raising awareness of Alexandra Palace, highlighting the restoration of the old Victorian theatre in its East Court, and helping to raise funds, LCA said.
LCA director Jenna Goldberg, who is leading the account, told PRWeek the agency would promote Alexandra Palace via media relations and stakeholder engagement "to position the palace as one of London's most important cultural institutions".
Goldberg said: "Ally Pally is a true public asset and we hope to help it take its rightful place among London's esteemed, world-class cultural institutions."
The agency will work alongside the Alexandra Park & Palace Charitable Trust's in-house team, which will be handling social and digital channels, Goldberg added.
As part of the brief, LCA will also promote Alexandra Palace's upcoming events, including its summer festival and annual fireworks display in November.
The theatre and East Court are due to re-open in autumn 2018.
LCA, which ranked 71st in the 2016 PRWeek UK Top 150 table, is specialises in projects in the capital. Its clients have included the Southbank Centre, the Museum of London, and the Young Vic theatre.