What is a lingering effect?
It's a player-made term for an effect which has already resolved/applied, and is still applying. EG 1: Card Trooper's "this card gains 500 ATK for each card sent to the GY this way".
EG 2: Gaia, the Polar Knight's "that target gains 500 ATK until the end of your opponent's turn." EG 3: Forbidden Lance's "that target loses 800 ATK, also, until the End Phase, it is unaffected by the effects of other Spells/Traps." EG 4: Double-Edged Sword Technique's "During the End Phase, destroy them, and if you do, take damage equal to those destroyed monsters' ATK." EG 5: Mechquipped Angineer's "change it to face-up Defense Position, and if you do, it cannot be destroyed by battle or by card effects this turn"
Exclusively Self-Applied lingering effects
Lingering effects can never (usually) be negated nor affected by anything. This means that if you resolve Spellbook of Power, and later Forbidden Lance that same monster, it doesn't lose the 1000 ATK gained from Spellbook of Power. However, this doesn't apply to lingering effects which could only ever affect the card itself causing the lingering effect. EG: Card Trooper resolves, and skill drain is later activated. Card Trooper's effect could only ever affect itself, so it's negated. EG 2: Gaia the Polar Knight's 2nd effect resolves, and skill drain is later activated. Gaia effect could have affected another monster, so it's not negated. It continues applying.
EG 3: A monster is affected by Forbidden Chalice, then later by Forbidden Lance. Lance can't make a monster unaffected by a lingering effect, so it loses 400 (+400-800), has its effects negated, and is unaffected by any Spells/Traps (other than lingering effects!) EG 4: A monster summoned by "Double-Edged Sword Technique" is Lanced. Lance can't make a monster unaffected by a lingering effect, so it's still destroyed in the End Phase.
EG 5: Mechquipped Angineer targets any monster (even itself), and is later Chaliced.
Chalice can't negate an already applied lingering effect, so Angineer's effect still protects the monster (even if it targeted itself, since it could have affected something else).