I assume that by "actually", you really mean "original", since both Microchip and TI actually make the part (as in, factually both manufacture them now). In fact, you missed one: STM released their LMC7101 just recently in 2020!
Anyway, the answer as to which of TI and Microchip made it first is: neither (if we are being pedantic) or TI (if we include acquisitions)
First, Microchip's datasheet has a revision note stating the conversion from Micrel to Microchip format. This means that their version was originally made by Micrel, a company Microchip bought. If we search for the Micrel datasheet, we see it's from September 1999. Note that the Microchip and Micrel datasheets also expressly state that the chip is intended to be drop-in compatible with the National Semiconductor part. That's a big hint that National Semiconductor was the original manufacturer.
Second, if you look at the TI datasheet, in its revision history, it states it was converted from National Semiconductor to TI format. National Semiconductor (Nat Semi for short) was a huge semiconductor company TI bought. If we search for the Nat Semi datasheet, the earliest one I found was from March 1995, but since it has no revision history, we don't know when it was first released. It could very well be older, but I doubt it since pre-1995 Nat Semi databooks don't mention it. A text search on archive.org also finds no mention earlier than 1995, and a 1995 ad listing it among "National's latest wave of analog innovations".
Furthermore, "LM" is one of the traditional prefixes for Nat Semi parts, so it's almost certain they created the original. Micrel used the MIC prefix for its chips.