Lionel made two very different O-27 Texas Specials, one very good quality and one much poorer. Recommendations will be different depending on which one you have.
The better loco was an O-27 single motor incarnation of the O gauge F-3 that came as an A unit and B unit set numbered 2245. Cleaning and fresh lubrication may help an ailing 2245. You need to use grease below the motor where the worm meshes with the worm gear. Power tool gear box grease sold for use in electric drills, etc. is good for this, and Vaseline can be used in a pinch. Light sewing machine oil is best for the wick on the top of the motor and for the axle bearings, and household oil like 3-in-1 is an adequate substitute.
The poorer locos were the O-27 Alco FA A-A sets numbered either 210 or 211. The more likely problem on the 210 or 211 won't be solved by lubrication - these exceedingly cheap units used an motor truck chassis built up from aluminum stampings held together with tab in slot joints that were "staked" to stay together. With age and use, the soft aluminum lets more and more play develop at these joints, so the whole frame slips out of square causing binds in the mechanism. This is near fatal - sometimes one can square up the units, use a hammer and punch to tighten the staked joints, and then add super glue along the seams to try to hold it in alignment, but this fix may only hold up for a Christmas or two.
Thank you very much for the detailed helpful information.
Unfortunately I checked the numbers and I have the cheap 210/211 versions. I may need to start looking for an affordable and hopefully more reliable MTH diesel replacement to pull my passenger trains soon.