This is from the John Sykes website gear section. Just look it up on Google. He uses a second LP custom most of the time. It's an old beat up thing, but man he has some tone! Here's the text about effects though and preamps, etc, from that era..
AMPS: John uses Marshall amps and Mesa Boogie amps. For the last ten + years of Thin Lizzy tours or Sykes tours, John has been plugging his Les Paul straight into one 50 watt JCM 800 Marshall head running in to one Marshall 4x12 (or one of his custom-made made 4x12's). A back-up 50 watt JCM 800 Marshall and 4x12 are also on stage ready to go should the first amp go down.
For much of the Whitesnake
'87 album and first Blue Murder album John used 2 Mesa Boogie Coliseum heads. These amps have a Mark III pre-amp section but use six 6L6 power tubes--giving the amps180 watts each! John also owns several Mesa Boogie Mark IIC+'s, Mark III's and some rack mounted Mesa Dual Recto heads. Other Mesa Boogie equipment includes a Tri-Axis preamp and a Strategy 500 Power Amp.
For speaker cabinets, John uses Marshall 4x12 cabinets, Mesa Boogie metal grill "Half Back" 4x12 cabinets, Mesa Boogie 4x12 Recto cabinets and some custom made 4x12 cabinets.
EFFECTS: The rack setup used during the later Blue Murder days included a Mesa Boogie Dual Recto head, a Mesa Boogie Tri-Axis Preamp, a Mesa Boogie IIC+ head, a Mesa Boogie Strategy 500 Power Amp, a rackmounted Dunlop Crybaby, a Lexicon PCM 41, a Lexicon PCM 70, and an H&H V800 Power Amp.
STRINGS & PICKS: John uses Ernie Ball Strings -- "Regular Slinkys" or "Reinforced Plain Steel" gauged at .010 to .046 (thanks to Derek Brooks for his help). He also uses Dunlop 1.14mm Tortex picks