The goal for Black in breaking the London System is to remove White's dark bishop from the game. This is present in almost every losing London System. Hikaru Nakamura plays the London, and makes it very clear he is not willing to trade his dark bishop - even going so far as to play h3 with the sole intention of hiding the bishop on h2.
To break the London, trap / trade the dark bishop.
Warning: This may contain multiple diagrams to display a progression of attacks and also possible positions
With regards to your exact example,
1. d4 d5 2. Nf3 Nf6 3. Bf4 c5 4. e3 Qa5
Let me just stop you there. You are down a decent amount in this position, and are looking at dropping a pawn. I understand that you want to get into a game which is not closed, but that is still possible without being hyper aggressive.
Lets get back to where you have a chance to start being aggressive and make a move which is subtly aggressive. I know it may not seem like it, but e6 here is very strong
1. d4 d5 2. Nf3 Nf6 3. Bf4 e6
e6, but whhyy
e6 allows you to begin to exert some control over the dark squares (which are White's weakness as their bishop cannot contest on them). It allows for a responsive aggression. Let us look at a few of the responses available.
1. d4 d5 2. Nf3 Nf6 3. Bf4 e6 4. c4 Bb4+
Nice, White tried to play into the Queen side and you got in a check (potentially White will trade their dark bishop in defense, but don't count on it). More than this, you gained a tempo, and can castle before White can; all while White's kingside is all locked up.
1. d4 d5 2. Nf3 Nf6 3. Bf4 e6 4. e3 c5
White was trying to keep a closed position but this actually results in a torn open one. Now if White defends with 5. c3 Black can begin to really open this up, and hopefully trade off White's dark bishop. 5. c3 Nc6 will open the board up and still be in Black's favor positionally.
Remove White's dark bishop
Consider this situation:
1. d4 d5 2. Nf3 Nf6 3. Bf4 e6 4. e3 c5 5. c3 Nc6 6. Nbd2 Be7 7. Be2 Nh5
White's dark bishop is toast, the game is open, and you have sacrificed neither material nor position. Game on!
Even if you do not choose to be so aggressive here, you have most certainly opened the board up and prevented a closed position.