Для кого-то это пустяки, мне же пришло время поставить жирную точку и НИКОГДА больше не путаться...

Lay - Laid - Laid → SVO (Subject + Verb + Object! + Preposition on/in/across/against)

for beautiful speach:

lay smth at smb's door - to say that someone is responsible for smth bad that has happened

lay the blame/responsibility (for smth) on smb - almost the same as previous, just negative stuff is not obligatory

lay charges (or bring charges) - BrE to officially accuse smb of a crime

lay claim to smth - to state that smth belongs to you

lay smth bare - to make smth known that has been hidden or secret

would lay money/odds/a bet on smth - to be very confident that smth will happen

lay smb to rest - to bury smb's body in a ceremony after they have died

not lay a finger on smb - to not hit or harm someone in any way

get laid - to have sex NEVER USE IT, very impolite and emberrassing!

phrasal verbs with lay:

lay aside or lay by - to keep or save smth, especially money, so that you can use it in the future

lay before - to offer smth tosomeone to study, discuss, approve etc

lay down - to put smth down to show you are finished with it, for e a weapon or a tool

lay into smb - informal to attack someone physically or criticize them angrily

lay off - to end someone's employment, especially temporaritly, because there is not enough work for them

lay on - BrE to provide smth such as food, service etc especially without charging for it

lay it on a bit thick - informal to make smth such as your admiratio for someone or their achievements eem greater or more important than it really is in order to impress someone

lay out - many very interesting meanings, look it separately

Lie - Lay - Lain → SVP (Subject + Verb + Preposition in/on etc)

for beautiful speach:

let it/things lie - to not do or say anth because you might mkake a difficult situation worse

lie ahead/before/in store - if smth lies ahead, it going to happen to you in the future

lie at the heart of smth - to be the most important part of smth

lie at the root of smth - to be the cause of smth

lie heavy on smb - formal to make you feel unhappy (Feelings of guilt lay heavy on him)

lie in state - if the dead body of an important person lies in state, it is put in a public place for people to go and look at (Ленин рулит)

lie in wait for smb - to hide s that you can attack someone when they pass you or if smth unpleasant is lying in wait for you, it is going to hapen to you

lie low - to hide or try to avoid attracting attention to yourself, because someone is trying to find you

phrasal verbs with lie

lie in - BrE to stay in bed in the morning for longer than usually

lie behind smth - to be the real reason for a decision or action

Lie - Lied - Lied

использовать to tell a lie or tell lies or tell smb a lie и не париться

lie through your teeth - say smth completely false

P.S. источник - Macmillan English-English dictionary for advanced users + Oxford phrasal verbs (выборка по принципу, что мне нравится)