Can I get evicted for one late rent payment in Texas?

You appear to now be current on your rent.  Consequently, you may able to ward off eviction litigation if you engage your landlord in mediation  before an eviction complaint is filed.  Mediation is a confidential process used to resolve conflicts in an amicable manner. A landlord-tenant attorney can serve as your mediator and facilitate a discussion with your landlord to try to resolve concerns s/he may have regarding your tenancy.  Or, your attorney can identify an appropriate third party mediator, educate you about the mediation and process, and represent you during the mediation.

If your landlord still attempts to evict you, your attorney will advise you regarding  available defenses and evidentiary requirements.  Defenses will be either procedural (the eviction complaint was improperly brought before the court) or substantive (the eviction suit is invalid because you have not violated the lease agreement).  Procedural defenses include deficiencies the notice to vacate; premature filing of eviction action; improper delivery; premature notice to vacate; and failure to give tenant an opportunity to correct the alleged lease violation.  A tenant can also assert that an eviction is substantively invalid due to the landlord’s waiver (e.g., failure to consistently force the allegedly violated lease provision), prevention, discrimination or retaliation. If you are behind in your rent when the eviction notice is issued, you should attempt to pay the money due but your landlord is not obligated to accept it.  Even if it is accepted, the eviction action is ongoing until the court finds that the case has been dropped.