Review of an existing Lease on a Flat

Property Investment

I am considering buying a ground floor flat that is part of a three storey Edwardian semi. The flat is Leasehold with 960 years left on the 1,000 year lease and it is a peppercorn rent. The Freeholder lives in the Maisonette above.
What I want is a legal review of the Lease as there are clauses that concern me regarding access and also there appears to be no maintenance plan or funds for repairs. There is no management company involved.
The Lease is 40+ years old and I want to know what terms and restrictions would now be considered overbearing, unsuitable or obsolete and how I might negotiate or change them.
If I decide to go ahead with the purchase I want to fully understand all aspects of the lease and also use any leverage I can to reduce the price.

I have no problem paying for the legal advice but what would I need to ask of a Solicitor? Is there a term for this type of legal request?
I normally use a conveyancing firm for my property purchases but they can't provide this type of service.
Thanks