Can I use Θ if tightest lower and upper bound are not the same?
When analyzing the asymptotic running time of an algorithm where the tightest lower bound and upper bound are not the same, is it bad to denote the running time in theta notation? 


Do you mean to say that we can only prove an $\Omega(f_1)$ and an $O(f_2)$ bound, respectively, on the same cost function (such as "worst-case running time)? Then yes: you can only use $\Theta(f_1) = \Theta(f_2)$ to combine the bounds if, well, $f_1 \in \Theta(f_2)$.

If you mean to say that best case and worst case have different growth rates, then that's a different issue: "lower bound" and "best case" as well as "upper bound" and "worst case" are not the same concepts! You can have $\Theta$-bounds for either case, but they still don't combine in a meaningful way since they are talking about different cost functions.


  Also, if an algorithm has a running time of theta(n), is it safe to assume that the upper and lower bound are the same?


That's not a "safe assumption", that's the definition of $\Theta$.

I suggest you revisit the definitions of the different Landau symbols and the basics on how to use them in algorithm analysis. Maybe start reading at our reference question.