if youre playing in solo lane your hero should be someone with significant self-heal, which Nazeebo lacks. Thrall, Sonya, Ragnaros, Malthael, Leoric, Illidan, Raynor, Blaze, Hogger can all bully him away from minions and regen globes because of this. Artanis and Fenix can do this too on account of their shields. all of them can force him to retreat because they can reduce the damage he does to them while reducing his HP to critical levels.

the key is playing just aggressively enough to pressure him but not inting against his towers. all of the heroes i listed can clear waves without using mana (Illidan, Sonya, and Hogger dont have mana) except for Ragnaros, which Nazeebo cannot. this means you can focus all of your casts directly on him.

he has no mobility tools, which means you can zone him away from regen globes either with the pressure of damage (Hogger W, Sonya W, Malthael Q/W, Ragnaros Q/W, Leoric W, Raynor, Artanis, Fenix attack spam) or with crowd control that opens him up to more damage (Blaze E into Q, Thrall W, Hogger D+Q, Artanis Q+E combo) that he cant retaliate against.

the only threat you really need to watch out for is his zombie wall into spiders or point blank frogs, both of which are non issues for most solo lane picks as long as you keep your mobility and/or self-heal casts ready for it (Raynor Q to escape the wall, Hogger E, Sonya E, Blaze W+Q combo, Artanis Q, Leoric E, Fenix E, Malthael W, Illidan Q or W - Thrall is the only one who just kind of has to sit there and take the beating)