It would be interesting to see why he left, if in fact he has, before speculating on any destination for Lashley.
If it was WWE's decision (for such things as steroids, bad attitude, etc.,) why would TNA want him? I'm not accusing him of any of these things, I'm simply speculating. In the days of steroid controversy and new drug testing programs, you have to wonder if TNA would want to sign someone who appears to be the poster boy for steroids.
If it was Lashley's decision, what happened? If it was a heat of the moment, pissed off situation, he shouldn't leave as he will be burning his bridges back to WWE if he wishes. If it was a well thought out decision, he may want to leave and not be worried about coming back.
I can't help but wonder if he was supposed to be HHH's mystery opponent at Raw this week, and creative wanted him to job to HHH like everyone else, and he didn't want to do it upon returning after a injury break of several months, so he got pissed off and walked. That's another discussion for another day.
I think jumping to TNA would be a bad move for both sides. It would be career suicide for Lashley, as he'll ultimately go down with the sinking ship, as will Angle, Cage, Booker, and all the others. Bad for TNA as well. To have any chance to survive and prosper, TNA has to distance itself from WWE, not directly compete with it. TNA will have a hard time competing head to head, regardless of the product, because of money. Talent, storylines, mic skills all aside, money is what drives the business, and TNA cannot go head to head with WWE for this reason. People here always praised TNA as being a viable, better, and unique alternative to WWE. But TNA has recently become a watered down poor copy of WWE, recycling WWE rejects and following equally poor storylines. This is not to criticize TNA, I'm not bashing their product. But if you look at TNA these days, it's not different from WWE, it's just a cheaper rip-off of them, and if this continues, it will fail. Instead of pushing Samoa Joe, AJ Styles, and others as true wrestlers not bogged down by a lousy creative team, TNA has fallen into the same trap as WWE. Signing Lashley will just perpetuate this, pushing home grown guys farther down the ladder, and bringing in yet another WWE reject. Bad move for either side IMO.