Doing logical operations on Port PINS in Assembly
After looking through this I've understood enough to show how \$\text{LED}_0\$ and \$\text{LED}_1\$ can be made, which should show enough for you to implement the other two. 

As you can see, \$\text{LED}_0\$ depends on three bits, the easiest solution would be to use temporary registers while you are manipulating the data from \$\text{PA}\$ and then set \$\text{LED}_0\$ once you're done. 

Here's one solution for the first two bits, it's not efficient/optimized, but it will make you understand what I'm doing. I will write PA = Port A since that's what you've written in the comments to your question. 

MOV TRA,PA // Copy contents from Port A into a Temporary Register A
MOV TRB,PA // Copy contents from Port A into a Temporary Register B
MOV TRC,PA // Copy contents from Port A into a Temporary Register C

LSR TRA //Move all bits once to the right in TRA, so bit1 in TRA is now in bit0

LSR TRB 
LSR TRB //Move all bits twice to the right in TRB, so bit2 in TRB is now in bit0

LSR TRC 
LSR TRC //Move all bits three times to the right in TRC,
LSR TRC //so bit3 in TRC is now in bit0


AND TRA,TRB //AND TRA and TRB together, bit by bit and save the result in TRA
OR TRA, TRC //OR the new TRA with TRC and store the information in TRA

ANDI TRA,1 //AND TRA with 0b00000001, in other words, remove the mess in other bits
MOV LED,TRA //copy TRA into your LED register

//Now, you're ready for the second bit for your LED register
//As you can see, It's PA1, PA2 and PA3 again, PA2 is still in TRB and 
//PA3 is still in TRC, PA1 is demolished, so we need to update TRA again

MOV TRA,PA // Copy contents from Port A into a Temporary Register A

LSR TRA //Move all bits once to the right in TRA, so bit1 in TRA is now in bit0

COM TRB //Make TRB into NOT TRB
OR TRA,TRB //OR TRA with the inverted TRB
AND TRA,TRC //AND the new TRA with TRC

ANDI TRA,1 //AND TRA with 0b00000001, in other words, remove the mess in other bits
LSL TRA //Move all bits in TRA one bit to the left
OR LED,TRA //Move whatever information is in bit1 in TRA into LED at bit1

//Now you're ready for the other two bits


This should definitely get you started. 

Remember that you probably want PA to be PIN_A, PIN_A usually corresponds in assembler language to the input of PORT_A.

If you want to optimize the code, then never move things into TRB and TRC and make TRA move around, it should lead to more efficient code, and use multiplication by \$2^n\$ to copy data into the multiplication register and rotate by \$n\$ to the left. So just rotate cleverly with the multiplication and look at the high byte of the multiplication register and you will have your rotated information there.