Loves me, loves me not

Pyth, 54 53 51 50 48 bytes

pj+*3\.bm+W~!Z"Loves me"" not"+3O18@".!"Z%hZ"</3

CJam, 53 50 49 bytes

Thanks to Dennis for saving 1 byte.

Imr3+{"Loves me"X!:X" not"*'.3*N}*&"!."X=N'<'/X*3

Test it here.

Explanation

The code just dumps the string in bits and pieces onto the stack, which is printed automatically at the end of the program:

Imr3+         e# Generate a random number in [3,20]
{             e# Execute this block that many times.
  "Loves me"  e#   Push "Loves me", we always need that.
  X!:X        e#   Toggle X (initially 1) between 0 and 1 and leave it on the stack.
  " not"*     e#   Repeat " not" that many times, removing it on every other line.
  '.3*N       e#   Push "..." and a newline.
}*
&             e# Set intersection of "..." and newline, turning them into an empty array.
"!."X=        e# Select "!" or "." based on the last value of X.
N'<           e# Push a newline and "<".
'/X*          e# Include "/" or not depending on the last value of X.
3             e# Push a 3.

Brainfuck, 2766 bytes (currently invalid)

Just because. I'll add an ungolfed version later.

Code

>+<+[>[>[-]+<-]>[<+>>+[->,----------[<+>[>>>>>>>>>+<<<<<<<<<-]>>>>>>>>>[>+<<<<<<<<<<+>>>>>>>>>-]<<<<<<<<<[>>>>>>>>>+<<<<<<<<<-]]<]<-]>>>>>>>>>>>>>>[<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>-]<<<<<<<<<<<<<<<[>[-]+<-]>[<+>>>>>>>>>>>>[<<<<<<<<<<+>>>>>>>>>>-]>[<<<<<<<<<<+>>>>>>>>>>-]<<<<<<<<+++++++[<+++++++++++>-]<[<<[>>>>>>>>>>+<<<<<<<+<<<-]>>>[<<<+>>>-]<<[>>>>>>>>>+<<<<<<<+>+<<<-]>>>[<<<+>>>-]<[>>>>>>>>+[<<<<<<<+>+>>>>>>-]<<<<<<[>>>>>>+<<<<<<-]+<[>-<[-]]>[>>>>>+<<<<<-]<<-]<-]++++++[>++++++++<-]>-[<<[>>>>>>>>>+<<<<<<<<+<-]>[<+>-]>-]<<<[-]>[-]+++++[<+++++>-]<[>>>>>>>>>>>+[<<<<<<<<<<+>+>>>>>>>>>-]<<<<<<<<<[>>>>>>>>>+<<<<<<<<<-]+<[>-<[-]]>[>>>>>>>>+<<<<<<<<-]<<-]++++++[>>>>>>>>>>+++++++++<<<<<<<<<<-]>>>>>>>>>>[<<+<<<<<<<<+>>>>>>>>>>-]<<<<<<<<<<[>>>>>>>>>>+<<<<<<<<<<-]>>>>>>>[-]>[<+<<<<<<<+>>>>>>>>-]<<<<<<<<[>>>>>>>>+<<<<<<<<-]>>>>>>>>>[-]++++++++++++++++++++<<[<<<+>>>-]>>[<<<<<<<<+>+<<+>>>>>>>>>-]<<<<<<<<<[>>>>>>>>>+<<<<<<<<<-]>>[>>[<+<<<+>>>>-]<<<<[>>>>+<<<<-]+>>>[<<->>>-<<<<->>>[-]]<<<[>>[-]+<<-]>>-]>>[>>>-<<<[-]]<<<[-]>>>>>>>>[-]<[>+<<<<<<<<<+>>>>>>>>-]<<<<<<<<[>>>>>>>>+<<<<<<<<-]>>>>>>>>>>>>[-]+++<<<[<<<<<+>>>>>-]>>>[<<<<<<<<<<<+>+<<+>>>>>>>>>>>>-]<<<<<<<<<<<<[>>>>>>>>>>>>+<<<<<<<<<<<<-]>>[>>[<+<<<+>>>>-]<<<<[>>>>+<<<<-]+>>>[<<->>>-<<<<->>>[-]]<<<[>>[-]+<<-]>>-]<[>>>>>>>>-<<<<<<<<[-]]>>>[-]>>>[<<<<<<<+>>>>>>>-]<<<<<<<[>>>>>>>-<<<<<<<[-]]>>>>>>>>>[<<<<<<<<<+>+>>>>>>>>-]<<<<<<<<[>>>>>>>>+<<<<<<<<-]<[>>>>>>>[-]-<<<<<<<[-]]>>>>>>>[>>>>>>+<<<<<<<<<<<<<<<->>>>>>>>>[-]]<<<<<<<<-]>>>>>>>>>>>>>>>[<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>-]<<<<<<<<<<<<<<<<[>[-]+<-]>[<+>>+++++++++++[>+++++++>++++++++++>+++++++++>+++>++++<<<<<-]>-.>+.+++++++.>++.<---.>>-.<<------.>.>>++...[-]<[-]<[-]<[-]<[-]<++++++++++.[-]>>>>>>>[-]>[<+<<<<<<<+>>>>>>>>-]<<<<<<<<[>>>>>>>>+<<<<<<<<-]>>>>>>>->[-]<[>+<-][-]>[<+<<<<<<<+>>>>>>>>-]<<<<<<<<[>>>>>>>>+<<<<<<<<-]>>>>>>>>>[-]<<[<<<<<<+>>>>>>-]->>[<<<<<<<<-<+>>>>>>>>>-]<<<<<<<<<[>>>>>>>>>+<<<<<<<<<-]>[>>>>>>+<<<<<<[-]]<->>>>>>>[<<<<<<<->>>>>>>-]<<<<<<<[>>>>>>>+<<<<<<<-]>>>>>>>[>>>>>>>>+<<<<<<<<<<<<<<<<<->>>>>>>>>[-]]<<<<<<<<-]<[>[-]+<-]>[<+>>++++++[>++++++++++<-]>.---------.[-]<<<-<->>-]>>>>>>>>>>>>>>>>[<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>-]<<<<<<<<<<<<<<<<<[>[-]+<-]>[<+>>+++++++++++[>+++++++>++++++++++>+++++++++>+++>++++<<<<<-]>-.>+.+++++++.>++.<---.>>-.<<------.>.>.<<+.+.+++++.>>>++...[-]<[-]<[-]<[-]<[-]<++++++++++.[-]>>>>>>>[-]>[<+<<<<<<<+>>>>>>>>-]<<<<<<<<[>>>>>>>>+<<<<<<<<-]>>>>>>>->[-]<[>+<-][-]>[<+<<<<<<<+>>>>>>>>-]<<<<<<<<[>>>>>>>>+<<<<<<<<-]>>>>>>>>>[-]<<[<<<<<<+>>>>>>-]->>[<<<<<<<<-<+>>>>>>>>>-]<<<<<<<<<[>>>>>>>>>+<<<<<<<<<-]>[>>>>>>+<<<<<<[-]]<->>>>>>>[<<<<<<<->>>>>>>-]<<<<<<<[>>>>>>>+<<<<<<<-]>>>>>>>[>>>>>>>+<<<<<<<<<<<<<<<<->>>>>>>>>[-]]<<<<<<<<-]<[>[-]+<-]>[<+>>++++++[>++++++++++<-]>.-------------.++++.<<<<->>-]<<]

Pseudocode

loop
    get a random byte
until random byte is >2 and <21

point to byte
[
    output "Loves me..."
    decrease byte by 1
    if byte is 0
        output "<3"
        exit
    eif
    output "Loves me not..."
    decrease byte by 1
]
output "</3"

Sample

When run, the program enters an interactive session waiting for input. Input should be a number. This number is used as a seed.

Seed: 1 (random number is 5, takes 218,168,042 operations)

1              
Loves me...    
Loves me not...
Loves me...    
Loves me not...
Loves me...    
<3             

Seed: 3 (random number is 20, takes 463,253,048 operations)

3
Loves me...
Loves me not...
(...)
Loves me...
Loves me not...
</3

I'd suggest that you do not seed with 6, as it takes 2,105,900,375 iterations to compute the result :).

Compiling / Running

You need a fast interpreter for this. No online interpreter I've tested could handle the execution speed. The ips (iterations per second) should be more than 100,000,000. So I came up with another solution.

This is a Brainfuck to C compiler written in Brainfuck. You can use any online interpreter to transpile my code to pure C. I suggest using brainfuck.tk. Paste my code in the stdin input, past this code in the code input:

+++[>+++++<-]>>+<[>>++++>++>+++++>+++++>+>>+<++[++<]>---]>++++.>>>.+++++.>------.<--.+++++++++.>+.+.<<<<---.[>]<<.<<<.-------.>++++.<+++++.+.>-----.>+.<++++.>>++.>-----.<<<-----.+++++.-------.<--.<<<.>>>.<<+.>------.-..--.+++.-----<++.<--[>+<-]>>>>>--.--.<++++.>>-.<<<.>>>--.>.<<<<-----.>----.++++++++.----<+.+++++++++>>--.+.++<<<<.[>]<.>>,[>>+++[<+++++++>-]<[<[-[-<]]>>[>]<-]<[<+++++>-[<+++>-[<-->-[<+++>-[<++++[>[->>]<[>>]<<-]>[<+++>-[<--->-[<++++>-[<+++[>[-[-[-[->>]]]]<[>>]<<-]>[<+>-[<->-[<++>-[<[-]>-]]]]]]]]]]]]]<[-[-[>+<-]>]<[<<<<.>+++.+.+++.-------.>---.++.<.>-.++<<<<.[>]>>>>>>>>>]<[[<]>++.--[>]>>>>>>>>]<[<<++..-->>>>>>]<[<<..>>>>>]<[<<..-.+>>>>]<[<<++..---.+>>>]<[<<<.>>.>>>>>]<[<<<<-----.+++++>.----.+++.+>---.<<<-.[>]>]<[<<<<.-----.>++++.<++.+++>----.>---.<<<.-[>]]<[<<<<<----.>>.<<.+++++.>>>+.++>.>>]<.>]>,]<<<<<.<+.>++++.<----.>>---.<<<-.>>>+.>.>.[<]>++.[>]<.>[.---->.---,....]

Download the source and compile it:

gcc.exe -c main.c -o main.o
gcc.exe main.o -o loveme.exe

You can also run a copy of the C code online here: via. CodingGround.

Optimizations

There is still some work to do, but the cell re-use is almost optimal.

Remarks

You can use words or phrases as a seed:

Programming Puzzles & Code Golf
Loves me...
Loves me not...
Loves me...
Loves me not...
Loves me...
Loves me not...
Loves me...
Loves me not...
Loves me...
Loves me not...
Loves me...
Loves me not...
Loves me...
Loves me not...
Loves me...
Loves me not...
Loves me...
<3