Can the landlord lock me out?
Yes, it is legal for the landlord to lock you out in certain limited situations, but the landlord must always provide written advance notice and also provide a key upon request. Texaslawhelp.org explains this more at this link.
For more advice on lockouts, check out this page from Austin Tenants Council.
Can the landlord remove locks and doors?
No. A landlord CANNOT remove doors, windows, locks, doorknobs, or any other appliance (such as a refrigerator or stove) supplied by the landlord because the tenant is behind on the rent. If a landlord removes one of these items for repair they have to make repairs quickly. For example, they should not remove a door over night without a replacement.
If the landlord illegally removes this property, you could also get a court order. If you get a court order, the landlord would have to return the property to you and you could end (terminate) the lease. In addition, you may sue the landlord for actual damages (the cost to you) + one month’s rent and $1,000 + reasonable attorney’s fees and court costs, minus any rent or other amount you owe to the landlord. See Tex. Property Code Section 92.0081(h).
For more on lockouts and your rights, check out this FAQ from Texas Rio Grande Legal Aid.