To avoid a relex lexicon, when I look for a word to make a basic root, I usually look in EN, IT and JP onlie dictionaries, and some others. Here they are:

• Etymonline: to grasp the 'real' and 'past' meanings of English words through their etymologies (words are often interwined with Latin or other European languages, so it's pretty enlightning)
  
• WordReference: for a translation between EN-IT-SP-FR to see if there are some notably differences among those languages.
  
• Jisho: this one is EN-Japanese. Even though one is not creating a Asian-esque conlang, I'd suggest to surf the dictionary sometimes: Japanese verbs are interesting, they can have very different nuances in logical and weird ways, a different perspective... Intriguing.
  
• Xiaoma: this one is EN-Chinese. I personally use it to check the correspondencies between Japanese kanji's and Chinese hanzi's, but of course can be used to draw some inspiration, too.
  

These are my 'basic tools'. However, I do not disdain Farsi, Sanskrit, Arabic, Bantu, Zulu, Swahili, Hindi/Urdu dictionaries, or any other natural languages.
Well, my method can be long and tiring, but that's the result for my WIP conlang, Shawi.