Can my former employer sue me for quiting and ask for reimbursement of training if I didn’t break any conditions on a non-compete contract?

They can only sue you for quiting and ask for reimbursement of training if there was some written employment conrtract which stated that under the conditions or circumstances that occured e.g. if you quit when and how you did, you would have to pay the employer some compensation or repay training costs. Without a contractual obligation to pay if you quit, there is no basis for seeking compensation employees may resign/quit whenever they like in the absence of a contract to the contrary and since the training is provided for the employer's benefit, there is no basis, outside of a contract, for seeking reimbursement for it.
There is a potential exception and basis for suing you IF it can be shown that you committed fraud in order to be hired--e.g. that you lied about your experience, education, or qualifications, and/or lied about you intention of keepng the job, in order to be hired and have the employer expend resources or money on you, such as if it paid you a signing bonus, paid to relocate you etc.--basically, the situation where you lied in order to get the bonus or relocation funds without being qualified for the job or intending to keep it past getting the bonus or relocation.