This is the earliest street directory I have found so far which also includes publican detail.
London Street Listings in 1832.
Lamb street, Spitalfields
Lambeth hill, Doctors common
Lambeth street, Goodmans fields
Lambeth walk, Vauxhall
Lambs Buildings, Bunhill row
Lambs Conduit passage, Foundling
Lambs Conduit street, Foundling
Lancaster place, Strand
Langbourn chambers, see Fenchurch street
Langham place, Portland road
Langley place, see Commercial road
Langley street, Long acre
Landsdown place, Brunswick square
Landsdown terrace, Lambeth
Lant street, Borough
Laurence Pountney hill, Cannon street
Laurence Pountney lane, Cannon street
Laurence Pountney place, Cannon street
Lavender yard, Rotherhithe
Lawrence lane, Cheapside
Lawrence street, Chelsea
Layton Buildings, Borough
Leather lane, Holborn
Leathersellers Buildings, London Wall
Lees Mews, North Audley street
Leicester place, Leicester square
Leicester street, Leicester square
Leicester street, Regent street
Leigh street, Brunwick square
Leigh street, Red Lion square
Leman street, Goodmans fields
Lemon street, Lomans Pond, Borough
Leonard square, Shoreditch
Leonard street, Shoreditch
Lily street, Saffron hill
Lime street, Fenchurch street
Lime street passage, see Leadenhall market
Lime street square, Leadenhall street
Limehouse, Union Dock
Liquorpond street, Hatton garden
Lisle street, Leicester square
Lisson Grove North, Marylebone
Lisson Grove South, see New road, Marylebone
Upper Lisson street, Edgeware road
Litchfield street, Soho
Little Britain, Aldersgate street
Little court, Castle street, Leicester square
Little Ormond street, Queen square
Liverpool Buildings, Finsbury
Liverpool road, Islington
Liverpool street, Kings cross, new road
Liverpool street, Finsbury circus
Lizard street, St Lukes
Lloyds row, St John street road
Loman street, Southwark
Lombard street, Borough
Lombard street, Chelsea
Lombard street, Fleet street
Lombard terrace, Chelsea
London Bridge, Southwark
London road, Southwark
London street, Fenchurch street
London street, Fitzroy square
London street, Ratcliff
New London street, Crutched friars
London House yard, St Pauls
Long alley, Finsbury
Long lane, Bermondsey
Long lane, West Smithfield
Love lane, Bankside
Love lane, Eastcheap
Love lane, Rotherhithe
Love lane, Wood street
Love lane, Shadwell
Love lane, Stockwell
Lovells court, Paternoster row
Lowndes court, Golden square
Lowndes terrace, Knightsbridge
Lucas place, see Bethnal green road
Lucas place, see Commercial road
Lucas street, Commercial road
Lucas street, Rotherhithe
Lucretia street, Lambeth
Ludgate Hill, Fleet street
Ludgate street, St Pauls
Luke street, Finsbury
Lumber court, Seven Dials
Lyons Inn, Strand
Lyon street, Holborn