Are you referring to Tytan 2.1 speakers?
Basically you are asking if a unknown quality sub is worth upgrading to a good quality sub. Well how can anyone answer that?
Certainly you can get the LSR 305's and try it with the sub you have.
Not the cheapest solution, but the JBL LSR 310 sub is pretty good as it is made to go with those speakers. Just as a sub there might be better subs for the money, but the LSR 310 lets you feed 2 channels over XLR or TRS to the sub and it will do the crossover, and send the needed signal on to feed the input of the LSR 305s. The one sub has outputs in stereo. So the crossover is handled in the sub for both the sub and the 305s which is a good way to do it.
You could get a Dayton sub for less and it is pretty good. It will take the input and roll off the woofer as needed. You still have to roll off the 305s to relieve them of the bass frequencies in some other way. You could set the sub cross over to fill in below the 305 while running it full range. This probably is going to put the sub in use at 50 hz and less. It could work, but relieving the 305 of everything below 80 hz is probably a better way to do it.
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