Admittedly, I have no experience with Varna, but in general TK is quite good at checking bags to final destinatin even when on separate tickets; at least when it is TK ->TK. It may make a difference that it is TK ->LH. However, it is entirely up to the agent that you speak to at Varna.

As stated above, TK is able to do it, but that doesn't mean that the check-in agents are prepared to do it for you. Be nice, explain that you prefer to stay airside at IST, that you will not have enough time to enter Turkey for re-check-in of your bags etc.- the check-in agent may take pity on you then. You need to show the e-ticket receipt for your onward journey with LH.