If you buy a gTLD domain through a registrar, your ownership of the domain is bound by the rules established by ICANN [1][2]. If you purchase an eTLD+1 [3] subdomain from omg.lol (as part of the offered services) you're not covered by [1][2] but instead by [4, Section 1.5 part B, Section 3.2 part A].

What this means is OP can arbitrarily shutdown their offering at their sole discretion and, as a result, you'll lose access to the eTLD+1 you've purchased (domain, email, all gone). However, if you purchase a gTLD domain through an ICANN accredited registrar, the registrar can't unilaterally do the same (even if the registrar implodes, you still own the domain and you can move it elsewhere).

[1] ICANN Registrants' Benefits and Responsibilities: https://www.icann.org/resources/pages/benefits-2013-09-16-en

[2] ICANN Registrar Compliance Program: https://www.icann.org/resources/pages/registrar-2012-02-25-e...

[3] https://jfhr.me/what-is-an-etld-+-1/

[4] Neatnik LLC (the company behind omg.lol): https://home.omg.lol/info/legal