Electronic – mbed SPI in Ticker function

I'd would rather use a shift register for this purpose (such as this one):

• they are cheaper than a microcontroller
• they are handier to drive a large number of led
• code will be located only on the Mbed. Think that you'll have to update code on both the Mbed and the ATtiny at some point: juggling with different microcontrollers, tools and languages may become a real hassle.

SIDE QUESTION: I'll be using the output with a DAC to produce an analog signal. Will I need to use a buffer in between, or are the pins guaranteed to output simultaneously?

You don't need a buffer in between, if you update all bits with just a single write to the special memory location (also known as register) controlling that I/O port.

The code in your question would not write all bits at the same time, but this will:

void sendByte(char value)
{ 
    uint32_t temp = DataPort;
    //clear the pins connected to D0..D7
    temp &= ~((1 << LCD_D0)
            | (1 << LCD_D1)
            | (1 << LCD_D2)
            | (1 << LCD_D3)
            | (1 << LCD_D4)
            | (1 << LCD_D5)
            | (1 << LCD_D6)
            | (1 << LCD_D7));
    //Write the value to the pins
    temp |= (((value >> 0) & 1) << LCD_D0)
          | (((value >> 1) & 1) << LCD_D1)
          | (((value >> 2) & 1) << LCD_D2)
          | (((value >> 3) & 1) << LCD_D3)
          | (((value >> 4) & 1) << LCD_D4)
          | (((value >> 5) & 1) << LCD_D5)
          | (((value >> 6) & 1) << LCD_D6)
          | (((value >> 7) & 1) << LCD_D7);
    //apply the new value to the I/O register. All pins are updated at once.
    DataPort = temp;
}  

You could also make the code more efficient by connecting the data lines to I/O pins that are mapped to sequential bits in the I/O port registers (e.g. D0 to PORT_A_3, D1 to PORT_A_4 ... D7 to PORT_A_10)

Then you could simplify that function to just

#define LCD_D0 3
void sendByte(char value)
{ 
    DataPort = (DataPort & ~(0xFF << LCD_D0)) | (value & 0xFF) << LCD_D0);
}  

When it comes to the overhead MBED, I have no idea.