Instead of setting the rotation to a fixed 1.5 degrees, create a variable with an initial value of 0, and rotate the object according to said variable*dt.
In addition, when left arrow is down, set 'turn left' to true AND increase the value of the variable by a fixed amount multiplied by dt (add 0.5*dt to variable).
To turn the other way, subtract instead of adding.
If you want to limit the maximum/minimum turning speed, whenever you would add or subtract to that variable, instead of adding or subtracting set the variable value to clamp(variable[+/-]<amount>,<min>,<max>) (see here for details).
don't forget to multiply stuff by dt, otherwise things will go really fast.
I hope this helped!